Innacurate speedo. 1990 Aus delivered NA.

So my speedo is reading higher than the car is actually doing.
I don't think it's by a small percentage either.
 
My car is a 1990 Australian delivered NA.
 
Recently the dash cluster was out of the car to swap out some crappy after-market LEDs for a set of original globes.
My cluster also had no lens when it came out. So when it was out I cleaned it up in preparation for clipping one on that I got off of a JDM turbo cluster.
 
Unfortunately when cleaning it I bumped the speedo needle and it went below zero.
It no longer wanted to sit back at zero... so I plucked the needle off and put it back on again.
When the cluster went back in I made sure that the speed sender cable was properly clipped back on.
 
To make matters worse I also swapped my wheels for a set that have different size tyres at the rear... so my rolling diameter changed.
 
I seriously have no idea where to start in figuring out how far out I am or how to sort this problem out.
Any ideas?

midmadness
To get a starting point, go for a drive with a GPS so you can get a 'calibration' of the speedo. 
 
 If there is a big difference, then something is definitely wrong with the speedo and I don't know what to do next other than take it to a specialist for repair (assuming the cable is OK etc).

 
I think you mean get a reference with the GPS rather than calibration. All GPS units I have used are within 1~2 kph of  'actual' speed so they are the best affordable reference. Thats your starting point, go for a drive at a few different speeds and check them against each other - if its the tyres/wheels throwing the speedo out the speed difference between GPS will change by %. (Say 10%) So if your GPS says 100kph the speedo will say 110kph - in theory drive at 1000kph GPS and the speedo will say 1100kph. That would mean that even though your speedo reads high as most do, its consistent and not rooted.
 
If the speed differences are not consistent the speedo is cactus. I wouldn't take it to be repaired myself - there's no shortage of speedos floating around and they are simple to swap over. Just annoying that you'll loose the odometer through bad luck.
 
What size combo are you running at the back? Thats a major factor.
 
 

Thanks for the advice so far!
 
I  dropped some numbers into this:
http://www.miata.net/garage/tirecalc.html
 

Specification  Sidewall  Radius  Diameter  Circumference    Revs/km  Difference
205/60-14         123mm   301mm     602mm         1890mm        529        0.0%
225/45-17         101mm   317mm     634mm         1993mm        502        5.4%
235/40-17          94mm   310mm     620mm         1947mm        514        3.0%

 
The top is what I believe the stock tyres were in 1990.
The second line is what I had when I bought the car.
The bottom line is what's currently on the car.
 
Based on this my speedo should be less innacurate now than it was before.
Unfortunately this is not the case.
 
My current set up is:

17x7 wearing 215/40R17
17x8 wearing 235/40R17
(Desmond Regamasters)