What size T-Bar Re-Rod stakes will I need for anchoring the drowner cable up on the bank for beaver? 18" or 24"?

Longest that will go in. Some places may take 36". Ive had beaver that refuse to go down the rod/wire pop the top stakes up if they can get above the stake. Luckily they tangled up nearby so i didn't lose the beaver and the rig... Made for an interesting time though.

I have and use some that are 48". Depends on how soft my anchor spot is.

Are disposable stakes a better option?

Probably not. Youll have the same sort ground issues with disposables. Plus you introduce some extra sloppynessnin the drowner with the disposables. Maybe if you make them adjustable it would help.

Much depends upon the ground you are working with. Some areas the ground is too soft to trust even a 5' t-stake much less a disposable so I have to be creative in anchoring my drowning rods. Recently I had one that I didn't feel comfortable using a 48" stake so added an extension cable and tied it off to a bridge. The next day proved it was a good idea to add the cable. Use what ever means it takes to anchor your traps.

Stake for an elephant...so you don't regret it later.

I cross stake with t stakes 24 to 32 seems good for most situations but I do sometimes run extention cable up the bank to hit stiffer ground.

Maybe try some wooden stakes. I have been using some 1x1 20'' stakes in lower ground and they seem to work pretty good. I make mine out or rough cut oak.