Good picture of the signal box diagram at https://flic.kr/p/23UAjdg. There is no signalled move at Dalwhinnie whereby an Up train can get on to the Down line. If I were investigating this, I’d be focussing on how/why that train (or at least, the vast majority of it) was where it ended up. It’s...
Existing signalling at Barrhead, while colour light, is worked from a lever frame, so there will be some degree of “resignalling”. The interlocking which currently works the East Kilbride branch is called “BARRHEAD”, presumably with this in mind.
Not current, but the Carlisle-based Derby Lightweight DMUs had Harker on the destination blind, which struck me as an odd place to terminate a service on a planned basis. Perhaps someone with local knowledge could elaborate?
Trawling the memory banks here, but when the Hairmyres loop went in, one of the driving factors was achieving a half-hourly “clockface” service, which simply couldn’t work without it. I think it ran on a 40 minute frequency prior to then.
The signalling plan I’ve seen is for full doubling. I would surmise, based on experience, that given that several bridges beyond Busby need to be rebuilt anyway, putting in double track is probably a relatively minor “extra”.