I can share that the compressor you stated there will not last for 37s.
Also, unsure of the source used for the spec numbers, but there is link for all ARB compressor specs:
http://store.arbusa.com/Assets/PDF/compressorTechnicalSpecifications.pdf
I used the that CKMA12 with a 5g tank for almost 2 years for 35s. Airing up at higher elevation takes longer = longer running time = impacts the duty cycle. I burned it up this past summer, yet did get it warrantied.
The factory pressure switch is like 90 on 110 off. Putting a higher cutoff switch increases running time.
Your goal is to reinflate "as quickly as possible". That is near impossible to gauge being purely subjective....
It took me (using said ARB) roughly 30 minutes to air up 35s from 12-15 psi up to 25-30 psi (driveable pressure)
at elevation (~+6000 feet). The elevation part is important to keep in mind (Bernoulli's principle). This took into account duty cycle time as a precaution.
Compared to your tire size and desired air up....yikes!
The tank size is not appreciable enough for all tires. It's only helpful for that first tire. CFM is the factor driving this.
This is also a good thread to look at if you missed it:
http://www.expeditionportal.com/forum/threads/117036-OBA
Hope that helps