FWIW most folks usually assign a locomotive the number that’s already on the engine…so Santa Fe 3622 becomes ID 3622. That way you don’t have to remember if your 2-8-2 is ID 282 or 2822 etc., it’s right there on the engine.
This is not an uncommon problem when your system of assigning long addresses is flawed (sorry UncBob).
As you have found out, as soon as you have two or more 2-8-2’s, you are in trouble using #282, #2882, #2828, #228, #2282, etc.
One solution is a mubering system for 2-8-2’s such as 2821, 2822, 2823, etc.
However, that numbering system won’t work for multiple 2-6-6-2 locos.
I follow the cab numbering system for prgramming long addresses. Of course, if your locos are unlettered and unnumbered, you still have problems. If you decal road names, why not also decal road numbers?
I had a similar problem when I ordered a pair of F7A locos from BLI Blueline with dummy F7B units. I wanted to build an ABBA consist with the option to run two separate AB consists. The F7A locos were both numbered 38. So, I programmed their long addresses as 381 and 382. I used a permanent marker on the bottom of the two units to mark the road numbers so i could distinguish one from another. You may want to do that on you 2-8-2 locos.