I thought it would be fine, yes. If not the HP, a lightly loaded TSX would certainly do the job. The TSX won't even expand below 1,800fps. If not that, a heavier bullet with Trail Boss would certainly kill rabbits without being explosive. I could get speeds down to 1,200fps, maybe lower.
Besides, previous responses have suggested 30-06, 45-70 and even 500 mag. 7-08 doesn't sound particularly over powered comparatively.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
You do not HAVE a soul. You ARE a soul. You HAVE a body.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.