No. It won't be compatible.
E series is not compatible with S series.
Talk to Nightrous. He knows his stuff.
Also if you are going to be stripping these boxes down make sure you don't ruin anything.
They are totally different in design. Require good quality pullers etc.
I wouldn't want to comment on drag coeffxzxs based on mass, torsion or any other BS.
Just please don't go using a bloody hammer an cold chisel trying to get them apart.

Thanks for all of your input everyone, it has been very useful.
 
A few things about me:
 
I have been modifying Japanese sports cars since 2004 and have built an SC22 RX7 Tarmac Rally car which is currently running in the CAMS Improved Production Series in NSW, a S5 FC3S RX7 Turbo that won the South Australian Tarmac Rally a few months ago as well as a 1984 Corolla Gymkhana car which doesn't seem to be able to win anything at all.....
 
So while I'm new to MR2's I'm not new to modifying. I have a very meticulous nature with an engineering background, so appreciate the finer details.  I seek out experts but if I can't find someone who can say "yes I've tried that and it does/doesn't work" then I will experiment.  If I get the diff gear set engineered for my car and it breaks at some point then I need to have a new one made up, if I can find an off the shelf solution and it breaks then I just get another one and put it in.  I enjoy this type of modifying, it's challenging and it excites me almost as much as driving at unsafe speeds around a racetrack.
 
I use professionals to do my work for me so I am not going to be stripping any gearboxes myself anytime soon, besides I like warranties.  :)
 
If you see me at the track I hope you will wander over and say hi, and please be courteous enough not to laugh at my driving (fake it if you have to).

OK. That is good to hear. The reason I was being a bit of a smartarse is that I've seen several perfectly good
Celica gearboxes ruined by people trying to dismantle them without using proper pullers etc. and chipping
gear teeth, crushing syncros etc. So unnecessary and a waste as these things are becoming scarce.
Enjoy the challenge.

Another option might be to look at the E250F gearing mixed with a Camry E53 gearbox (Came with pre-1994 3VZ Camrys).
 
It will bolt up to the adaptor you have, would require SW20 turbo drive shafts and hubs and would allow you to mix the E250F/E53 gears. I've seen this done with 3VZ Rav4, check it out here:
http://strav3vz.blogspot.com.au/2013/05/e53-to-awd-transmission-conversion.html
http://strav3vz.blogspot.com.au/2013/05/dissasembling-e250f-e53-transaxles-1.html
http://strav3vz.blogspot.com.au/2013/05/dissasembling-e250f-e53-transaxles-2.html
 
I believe if you can source an E53 and use the E250F 1st gear and diff, then use the E53 2/3/4/5 gears, this will give you a tighter box then the E250F. I was intriqued and came up with this table comparing S54, E53, E250F and a E53/E250F hybrid.
 

5th gear would let you cruise at 100kmh @ ~3500rpm, which will let you keep some fuel economy...
 
Infact, out of curiosity, I ran the numbers comparing the three 6 speeds and a hybrid of them and an E53/E250F is closer then those too.

 
Food for thought?

See what I mean. Talk to Knightrous.
Another thing that I've seen buggered up even by supposed gearbox experts is failure to realize that changing the number of teeth on one gear eg. ring gear on diff. Requires the corresponding output shaft to be changed also.
Same applies to the oil pump drive in the E series boxes.
I've had two characters ? with almost completed swapsies with just one slight problem. Unable to get two shafts parallel by about 20 mm. (Nothing to worry about).
Talk to Knightrous.

I get your concerns Falcon, which is why I felt to need to share a bit of my history so you guys know I'm not just some hack.  I'm very patient and meticulous and will follow a trail of breadcrumbs as far as it will lead me.  :)
 
Damn Knightrous!  If I don't owe you a carton of beer by the end of all this then there is no justice in the universe!
 
My research has indicated that the E53 and the S53 are the same box with different gearing, the S53 is the predecessor to the S54 and internally are fully compatible.  Does this sound right?  If so then your research would suggest that the E250F final gear set is a direct fitment into the S54?  I know there is no cheap option but I'm also balancing the cost V's delivery, I may have to sacrifice something to safe a few pennies.
 
Will I also need to address the driver side drive shaft clearance issue Thomas was faced with?
 
The E53/E250F hybrid DOES look like it would be an exceptional budget track day box, probably best bang for buck.
 
Also, I found some more interesting reading:
http://www.celicatech.com/forums/archive/index.php/t-54182.html?s=8f38b97d3909796140c2e5274c1010bf
 
There are definitely options out there, I find myself spending a lot of time on the Celica forums...  They do a lot of cool stuff to their cars.

I'm 99% confident that E series internals are vastly different to S series.

Not trying to shoot down ideas here, but after a few years in the MR2 game I am a strong believer of following the simplest route.

The simplest route to me appears to be an adapter plate and a 6 speed K20 box. You get very good ratios and a cruising rpm in 6th of 3200rpm at 100km/h.

The risk of mixing and matching internals is that you end up with two gearboxes in need of some repair, such as worn syncros or bearings, then you have to replace these parts. Labor time is going to be fairly expensive too.

If I was in your position I would buy the adapter plate, a good condition used K20 box and applicable driveshafts are needed to make this work. The only hurdle in this instance would be reversing the shifter cables on the gearbox end, however I am sure there is an aftermarket solution available.
 
Anyway, that's just my 2c. Feel free to take that as you please :)

sir_smeghed
My research has indicated that the E53 and the S53 are the same box with different gearing, the S53 is the predecessor to the S54 and internally are fully compatible.  Does this sound right?  If so then your research would suggest that the E250F final gear set is a direct fitment into the S54? 

 
I'm going to say no based on the following:
 
The E-series boxes all share a common diff size that can be swapped. You can take a diff from an E51 AW11 SC gearbox and fit it into an E153 SW20 Turbo gearbox. You can also fit it into an E58 AE101 Corolla gearbox.
 
None of the E series diffs work in an S-series gearbox. The only diff that does fit in an S series is a C-series. It's very common for people to steal a torsen diff from a C56M or C60 gearbox and fit it into an S54.
 
The E-series gearboxes feature an internal oil pump driven from the output shaft. The S-series gearboxes all rely on the diff flicking oil onto a catch tray. And since you require the output shaft to be swapped with a crown wheel for a diff swap (To maintain PCD and bearing spacing like Falcon mentions), you will not get that to work between an E250F and an S54...

Gotcha, that makes sense.  Whats confusing me is that the E53 and S53 transmission casings share the same part number (neither of which are actually stocked anywhere anymore).  I wasn't aware the E series boxes had an internal oil pump, do you know if it is possible to direct the transmission oil flow through a cooler?
 
I will also look into the K20 option but am pretty sure all of the 6 speed boxes are going to have the same issue, too long.
 
Any thoughts about the driver side drive shaft clearance issue?  Or is this not an issue with the turbo drive shafts?

If you have a look at my calculations on page 1, you will see the ratios are fairly close to the hybrid box. the K20 is 67kmh in 1st vs 53kmh for the hybrid box


2nd is 103kmh k20 vs 101kmh
3rd is 144kmh k20 vs 155kmh

As for coolers on E series boxes, there is a steel pipe which runs outside the case on the underside which provides some cooling, however you can splice into this and run an external cooler. This is what my used gearbox had when I first bought it