In regards to the Borg fighting against altKirk and crew, I have no problem with that. Enterprise
(which is still completely 100% correct in this timeline as well) already established Borg tech pre-TOS, so Kirk and company coming up against them would be perfectly acceptable.
But why not throw the TOS crew up against Cardassians? The 2009 movie confirms Starfleet has meet the Cardies at this point, and it would provide audiences with something they've never seen before (TOS era Cardassians) without it feeling quite so... contrived as bringing in the Borg.