6mm moose rifle?

At the ranges you're hunting I'd say go with whatever cartridge she's most comfortable making a flow up shot with if necessary. Going from a 77 grain tmk to an 88 grain tmk will gain you some penetration but I'm not sure by how much. Shot placement is the biggest key. 22 or 6 cal won't overcome a bad shot but either will work with good shot placement and a heavy for caliber bullet. Good luck and don't overthink it!
 
get her a 243 or 6cm and have her shoot lightly loaded 68 or lower bullets so she's confident. Then on opening morning, load the rifle with some medium/high powered 90gr ballistic tips (that you've zeroed privately) and she won't feel the difference when shooting big game.
 
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