A bigger unit will NOT fix the uneven temperature problem on the North side of your house. In fact it will probably make it worse due to shorter cycles. Ductwork is the most likely culprit here and will require repairs/upgrades. HVAC contractors generally don't like messing with ductwork because it's labor intensive and not very profitable, the lowest bidder will almost never do it.
Air handlers are typically available in whole sizes, a 3 ton is a typically a good match to a 2.5ton condenser. All compatible condensers and air handlers has AHRI ratings. Since you are considering Trane, also look at the American Standard which is basically the same thing. Pricing discussions aren't allowed on the site.