Motor pulley for an old Ingersoll Rand type 30 compressor

I have an old Ingersoll Rand Type 30 horizontal tank compressor that was given to me by my father-in-law. He jury-rigged a motor to drive it as it had no motor when he got it. The compressor has a 3 groove pulley but the motor was set up with 2 aluminum pulleys which lined up with the two outer grooves on the compressor pulley. This worked well for about 5 years but I continuously had issues keeping the belts tight enough to prevent slipping and the aluminum pulleys finally gave out. The pulleys were approx. 2.25” in OD. I have found 3 groove cast iron pulleys that will fit my motor but none that small; the smallest OD available is 3.75”. In reading another person’s solution here for their compressor motor pulley problem, I’m wondering if 3.75” may be too small for the intended design of the compressor…?
Here are the specs: The compressor is an Ingersoll Rand Type 30, size 5 & 3X31/2, Model 253, S/N 30T 115---
It was originally built/sold by Berg – DiMare & Berg Pumps, Air Compressors, Motors located (at the time) on Haverhill Street in Boston, Mass.
The motor on it (not original) is a capacitor start 5hp, 3450 RPM, 230 Volt with a 5/8” shaft.
Since it worked for so long with the small 2.25” pulleys, I’m pretty sure it’ll work fine with the 3.75” cast iron one as well, but I kind of wanted a better fit as to the size it should have.