Or instead of asking someone else on the phone, get out to the shop and measure what they actually are.Funny you have been using small based dies all this time and didn't know it but you criticize others for buying small base dies.
Anyone can find this info with just a few phone calls. Call every die company and ask to speak to the engineer. Ask them what their target design diameter for the dies are. Yes they all have tolerances and may be a little larger or small but they draw the dies to be made a certain size(target dia). Ben At Hornady has been making custom dies for me 50 at a time for years and Lonnie before him going back 15 years. Either on of those guys can tell you in 2 seconds .004 under minimum chamber size.
My Hornady 223 dies measure exactly the same at the base as my standard RCBS 223 dies. Not "small base" RCBS dies, but standard. My 6 PPC and Grendel die sets show the same results as well. The actual SMALL BASE dies are the only ones that measure smaller there. (Had to type that in caps so you could figure out which end of the cartridge it refers to.) We are not talking about shoulder diameter here, that is not the issue.
The Hornady dies I have are slightly smaller at the shoulder, but NOT at the base. That doesn't make them small base dies. Are you confused what "small base" means? It sure doesn't have anything to do with the shoulder of fireform rounds.