I'm neither a fan, nor opposed to the crossed cable idea. It's a matter of getting the best housing run while allowing them to flex nicely when the bars are turned. On my own bikes, I cross the housings past each other and back to the usual side (right rear). Yes they rub the head, bit a dab of clear paint protection tape handles that fine.

But getting back to the OPs problem.

The crossed wires should not affect shifting, and I'd look elsewhere. The first thing I'd look at is the rider. The front derailleur operates on the tight side of the chain, and upshifting requires lifting the chain against this tension. Many riders simply don't ease the pedal pressure off enough for the shift to happen. One give-away of the rider being the issue is a bike that shifts crisply on the stand, but not for the rider.

Other possibilities include, overly restrictive outer limit, derailleur alignment, FD cage too high, cable friction (often under the BB) and general adjustments not being spot on. Start by riding the bike yourself, or checking on a stand, and if necessary check every detail of the installation and adjustment until you identify the problem.