Not sure that your logic that TPE warrants something different to the 350s - given the stopping patterns they have, the units need to balance the long-distance nature of the route with the ability to have short dwell times where there are regular stops. It's the same issue XC has with some of their services or, for that matter, LM have with their London - Crewe service.
The stopping pattern of the Scottish services is InterCity - Manchester Picc, Manchester Oxford Road (ICs never used to stop, but that was I think platform length), Wigan NW, Preston, Lancaster, Oxenholme, Penrith, Carlisle, Lockerbie, Haymarket, Edinburgh. That isn't a regional express, it's InterCity, and is broadly the same as the VTs.
Something like a "Class 344", preferably 5 or 6x23m, would be ideal for these services. Perhaps Siemens might consider making an end-doored version of the new-generation Desiro? I saw some for the first time in Edinburgh last week, and the massive windows in the central section must make them feel lovely and airy. But preferably with the super-sized Desiro luggage racks remaining - my very large (but not overly heavy) case fitted nicely above my head.
Notably, the 1612 EDB-MIA yesterday, which I was on throughout except the last bit to t'Airport, suffered serious overcrowding as ever - but only from Lancaster to Preston. Time for more local services on this stretch perhaps?