I'd be wondering if you're underestimating the task of moving it all to the rear ?

Balance will depend on weight distribution....as well as suspension/chassis setup all round. So nobody can say whether it will end up better balanced or not...and even that is a very open to debate term, as every driver could have a different opinion.

If you get it wrong, it could be an ill handing POS, if you get it right, it might be fantastic.. But short wheelbase, mid engine....ever driven a MR2 ? I wouldnt call them well balanced, I'd say they're tail happy as fuck ( or go round in circles like fuck lol )

But yes mid engine will offer more traction, there is no doubt about that

If you've a good FWD setup all running and working....IMO if you're considering such a project, you'd be better buying another car and doing it rather than potentially destroying a fully working car.