Going back to Ken's original question about a 3.73...
Ken, looks like you are trying to pick up top end cruising speed. You have an answer to your 3.73 question. And finding a 3.90 might be a bit of a unicorn. Let's say a 3.73 was available...what would you pick up on top end at same RPM from your current 4.56? You would pick up 18.2%.
You would pick up 10% by switching to a 4.10.
How do you pick up the balance if you can't find higher gears? Increase your tire circumference. You can make very precise estimates if you know your current tire circumference versus a proposed circumference.
Here is cut and paste from something I posted a couple years ago that you might find helpful.
If you do either or both, and you want your speedo to be accurate, you will need to buy an easy-to-install adapter that can be custom built to your needs. I got mine from Jim Carter's.
I have a '57 3/4 ton with a 235, 4 speed SM420 and A/C. I think it is about max'd out with the 4.10 and the 8R19.5 tires. I find that I use the granny out of the hole when the A/C is running. The larger brakes on the 3/4 ton handle this just fine, but I would not be comfortable pushing top end any further.
The results listed below would not have any material difference if you find a 4.11 instead of a 4.10.
Hope this helps,
Matt
From an earlier post---
Several posts have inquired about actual performance increases when looking to increase top end. For those interested in my field test results...
Testing was done using a GPS and calibrating MPH on the GPS to the reading on my speedo.
Switching my '57 3600 from STA Super Transport 8x17.5 bias plies to Bridgestone 8R19.5 12 ply radials gave me a pick up of 10% MPH. (Good luck finding the 19.5" rims!) I anticipated an increase of 7.5% when I did the calculations based on published tire specs by both manufacturers (based on the difference in circumference), but actual increase was 10%.
Changing my 4.56 rear end to a 4.10 gave me another 10%, exactly as the math indicated that it would.
Independently, either of these alterations would pick up 10%. Doing both gives a compounding effect and actually picks up 21%.
Before the change, my comfortable highway cruising speed was 52 MPH. I can now run 63 at the same tachometer reading.