Sadly the Ps2 homebrew/emulation scene never really took off, even with the advent of the memory card exploits and even a special cd file system that tricks the ps2 into thinking a disk full of files (such as roms) is an audio cd thus bypassing it's protection. There was a tg-16 emulator for the ps2, but further development of it stopped early on, and as such it is not very good. I think the creator of that specific emulator got mad at some "lamers" or other typical drama and said he would no longer update the emu.
Also, sorry to burst you bubble Dreamcaster, but of the two tg-16/pce emulators for the dreamcast that I know of, neither are very good. Most games have glitches, or are slow, and iso's or cd games are very buggy. Trust me I have tried them.
Really the xbox is the route to go, if you have a xbox, computer, and the right screwdriver and some technical know how you can soft mod your xbox for free. I already tried it and it works great! If you want to know how, it's via the hotswap method and is a little annoying to do the first time, but after it's modded you don't have to fool with hotswapping again. If you want I could point you in the right direction on how to softmod a xbox yourself. Trust me if you can find a cheap xbox it's worth it.