Omni-Sentry, wrench [Because otherwise, it could interfere with the gunslinger if PDA.
[-]No dispenser! (Doable, just make dispenser death on creation.)
[+]Sentry has infinite ammo. This is doable. This command (sv_cheats 1;ent_fire !picker setbuilder !player;ent_fire !picker addoutput "spawnflags 8";ent_create obj_sentrygun;sv_cheats 0) sets the built sentry gun to have infinite ammo. Upon further inspection, sv_cheats 1/0 can be removed, for test servers. However, the sentry gun built cannot be upgraded, fixed by picking up and putting back down.
This uses the Ammo regen part of the dispenser.

Immortal-Sentry, wrench [Same problem as before]
[-] Teleporters and Dispensers destroyed on creation.
[+] Sentry is immortal, except to sappers [which will still destroy it, for ctf balance reasons.] This is possible as well. Using the same command as before, but edited. Simply replace "spawnflags 8" with "spawnflags 2".

One problem with both of these suggestions, I've checked that there are no stats for them. I've just put in stuff which shows they are doable. I know it's unlikely these will be added. But, if i hope and prey enough, it will happen.