Considering you are storing fresh cactus, there should be no problem in storing it for a long time if it's frozen. You can take it out to thaw at anytime.
Personally I've stored San Pedro and Peyote both fresh and dried in the freezer without any noticeable loss of alkaloids months later.
The cactus will however, as any organic material would, decompose at a faster rate if stored for a long time and then be brought out to thaw. So when you do take it out to thaw I'd advise against keeping it out for too long.
Whatever plant material I take out of the freezer I take immediate use off. Treat the matter with common sense and there should be no problem

How would you store chicken for a long time to keep the protein (denatured by heat) safe and then for how long could you keep it out while thawing without risking it going bad?

Same thing with cactus but with alkaloids.
Mad, bad and dangerous to know.
There's magic out there!