Any question answered...

I have Sram Apex on my cross bike, which has a long cage rear mech.

If I wanted to upgrade the mech, there are zero options within the road range as higher than Apex you only have short cage mechs.

So- would a Sram MTB mech work with my shifters?

Either change the cassette to a 28t max for use with a road mech or ask somebody who knows what they are talking about - I think SRAM 10s MTB mechs work with road shifters, but don't take my word for it. Older 9s speed ones definitely don't. Or just accept that you already have a perfectly decent groupset and ride the shit out of it instead of constantly trying to upgrade your bikes.