If you are very lucky I might still have the CAD drawing for the shroud on one of my computers somewhere.

Shweet thanks for the pics. That is a massive core! These ORB hose ends sound good, less pieces = less points of failure. I'd like to run the cooler with opening/hoses pointed towards the ground to reduce length but I can imagine how hard it would be to tighten the fittings especially since I have my alternator in the FWD position! Maybe a knuckle-type spanner would help reach in those tight areas

You wouldn't want to put the fittings on the bottom Tree as the oil will drain out when the engine is off.
Also means when you start the engine the cooler will need to be filled so will stuff around with your oil levels,

+1
For mounting the cooler fittings on top.
 
And yes, short handle spanners make it much easier to tighten the fittings.

You could also use 'crows feet' to tighten them.  Unfortunately the is no room for any of this with my setup and I think the ORB fittings are a great all round solution, I do however suggest you get some replacement seals to have onhand.
 
  I have an Earls catalogue I downloaded which actually has recommended torque specs for the different size fittings and crows feet are the only way I could think of to torque fittings...

I see, what about mounting it sideways?
When doing an oil change, how does one empty the oil cooler with the hoses mounted on top?

I don't think you would bother trying to empty it during an oil change. I never did. Its just like the oil that is trapped in the various nooks & crannies inside engine when you normally do an oil change.

Tri, mounting it sideways wont stop the oil draining out on shutdown - bad for dry starts.
Another benefit of having the fittings on top is if you need to remove the cooler, the oil won't spill everywhere.
 
I do remove my cooler to drain during oil changes, so it's lucky I like working on my car lol.
There is quite a bit of oil in the hoses as well as the cooler.
There are readily available fittings to close off the hose ends to help avoid a mess when they are undone. I find having these is well worthwhile.
 
I'm surprised you haven't mentioned if you have worked out how much your new system add to your oil capacity - another benefit.

I predict a 13 row will add about 1 cup more oil and a couple more ml in the lines depending on the length. Besides more oil meaning less temp or longer changes I don't really see any other benefit unless the increased capacity somehow helps with oil starvation during high g's, but I don't see how it would help in that sense since the oil is just circulating around at standard rate of the pump albeit with an extra external reserve i.e cooler
Capacity wise I guess when doing the oil change I'll just make sure I put in 4L and top up as I go lol
After having a look at the RHS vent area again it looks like the hoses might be pretty long from there so I might steal your placement idea Ian hehe or at least reconsider placement. Gen 3+ sump is also down the bottom so changing the oil filter I can inspect the cooler at the same time

My system holds 6 liters that is 50% increase, but I do have a much larger oil filter than stock as well.
 
I suspect your hose runs would be quite a bit longer with an underneath rear mounted cooler than a side vent mount.
And you would also have to route the hoses to avoid the drive shafts that also adds length.