I've never compared the big and medium sized blocks with external measurements. I think external lengths would be the best way to confirm what I assume, that there were three sizes of blocks, including the smallest blocks under 340 cid. Maybe we could get some measurements posted here that would be good reference for later.
The 250A and earlier engines had a 5.125" stroke and bores going up to 4.0" for a 386 cid. The 250A was preceded by the 362 cid, introduced in 1935. This size engine was common in the W22 series trucks and White cranked out a lot of them for 30 years. They had a 14" clutch.
The 260A and larger and later models had a 5.0" stroke. This size engine came out in the late 1940s. Bore for the 260A was 4.385" for 451 cid, and that block went to 4.75" for 531 cid. They had a 15.5" clutch.
White engine model numbers refer to when the design was introduced, and in the 1950s the last two digits preceded by a 3 or 4. There's little consistency.
White made a couple of main transmissions but most were Clark and some Fuller. 1950s and 60s Motors Manuals had the Model number conversions for White number to vendor number. One competitor info chart I have says the WC 28 used a Fuller 5A-65.
For auxiliary trannies White used Brown Lipe three speeds. White would badge them and give them a H prefix, for example I have a early 1940s 6H.
Jeff, you might just have to jack up a wheel (or push the truck a short distance) with the main in neutral and start spinning driveshafts to see if you have a .86 od or .70 od. For exactly one turn on the input, output shaft would be near 10 o'clock for .86, near 7 o'clock for .7 od.