I'm looking at a Scottish 400 next year and it is over 1100 miles round-trip to the start. Transporting the audax tandem (shortish 700C jobbie, no S&S couplers, wheels off is easy) by train would be preferable to driving as the car is insured for <5000 miles annually. Getting the tandem between London and Edinburgh by train might be doable but further north by Caledonian Sleeper or Scotrail doesn't look viable.
LNER, who replaced Virgin, still had some older trains on daytime services between London and Inverness. Iirc the 1200 from Kings Cross is normally one of these.
Zoomers replace the IC125 on the Chieftain on the 19th.
Most if not all East Coast Edinburgh services will be by then too.
Hire a van, and offer bike space for contributions getting bikes to Inverness on the train is tricky, getting them to Dingwall even trickier all due to only having 2 spaces a unit/set.
Your only hope of more space to Dingwall/Inverness is if the partly refurbished HST sets are running on the HML and even then you're chancing it.
Can you pack the tandem down to luggage size?
i.e. wheels off, bars turned, wrap up in a couple of bin bags and "it's a double bass honest"