Your allowed 2 cases/bags and hand luggage so no reason you couldn't take the wheels off and bin bag them and the frame separately as long as they are not longer than 1 metre. Get on the train early and dump the bags – then sit fairly far away in the carriage. I doubt they will care TBH…..
What luggage can I take on the train?
Each customer can carry, free of charge, three items of personal luggage – two large items (such as a suitcase or rucksack), plus one item of hand luggage. You can also take up to two dogs, or cats, or other domestic animals, folded prams, non-folding prams and carrycots, wheelchairs, including battery operated models where wheels are no larger than those on self-propelled wheelchairs, or any article which does not exceed 1 metre in any dimension and which can be carried by one person.
Items for which charges are payable: each additional item of luggage over the free allowance, each additional dog, cat or other small animal above the free allowance, each article exceeding 1 metre in any dimension but which must be capable of being carried by one person.
The charge for any item outlined above (except cycles) is half the adult fare appropriate to the type of ticket held for the journey per item – subject to a maximum charge (presently £5 single, £10 return). No further discounts will be available for Railcard or Season Ticket holders. Excess luggage charges do not apply to Caledonian Sleeper Services.
http://www.scotrail.co.uk/travelinfo/faqs.html