The first thing to do as you say 'we' is to travel after 9.30 am, and buy a Two Together Railcard- that gives you 1/3 off all train fares-
https://www.twotogether-railcard.co.uk/
Secondly totally forget about all the different rail companies. Just look for the trains that go from A to B.
Bath to Stratford is an awkward journey needing 2 changes- at Reading and Leamington Spa. Ticketing that can be complicated to save a few £ or easy. The easy way is just buy a full priced ticket from Bath with your railcard for £51.15 each.
To save a few £ train to Leamington Spa instead for £43.35 each, then a bus to Stratford every 30 minutes for £2 each, from outside the station (Man in Seat 61 won't tell you that as he doesn't use buses).
Stratford to Chester- train to Birmingham Moor Street, walk 300 yards up the road to Birmingham New Street, train to Crewe, change trains, train to Chester. Book a specific train ahead of time, advance fares on 15 May (sample date) tonight vary between £8.55 and £12.50 each.
Chester to Glasgow- again book a train specific Advance Fare- train to Warrington Bank Quay, change trains for Glasgow. £15.80 each
Glasgow to Edinburgh- buy on the day- £10.55
Edinburgh to York- Advance Train Specific Fare £28 to £34 each
York to London- Advance Train Specific Fare- Choose a train time that suits you- between £20 and £30.
Total train fares around £150 each.
Buy all the Advance Tickets on the LNER website. If you want you can specify that you have a railcard but don't need to buy it until you are in England, at Bath station, if you take the bus (coach) Heathrow to Bath.