That bypass line idea is unlikely to happen unless we get back to a world where the railway is capacity constrained and electrification is no longer the top priority. Partial electrification using BEMUs should simplify the Fife electrification by quite a bit. With traditional electrification, you'd pretty much have to electrify the Forth and Tay bridges as well as remodel Perth in order to get any real benefit. So, if you were to spend a big chunk of money to deliver some benefit sooner, it wouldn't be unreasonable to think about new tracks that would allow existing diesel trains to work more effectively. Electric or BEMU trains would still benefit from alignment upgrades but their faster acceleration means the improvement isn't quite as stark.
Leaving Perth mostly or entirely unwired until the remodelling is done seems perfectly sensible. That's the big benefit of BEMU: you don't have to wire up every last bit of track in order to run electric trains. The more wiring there is on the rest of the route, the less need there is to have it up in the station for trains to charge up before continuing. If that proves to be necessary, then partial electrification and other no-regrets work seems sensible.