When people say that services can't be lengthend because of the length of the platforms it annoys me as the alternative is more services which means more trains, more train crews and more signalling upgrades.
DMUs can have a extra carriage powered by AAs if necessary.
I think the first step is to properly segregate the local and 'inter city' operations on TPE north. 4 tph 'intercities' stop only at York or Hull/Brough/Selby - Leeds - Huddersfield - Manchester - with 2 tph to/from Liverpool. Stop trying to serve Manchester Airport, it just introduces unreliability, terminate the other 2tph into Piccadilly via Guide Bridge. This 4tph fast service is operated by 8/9 car units, apart from Huddersfield platform lengths at the other main stations must be adequate as they already handle trains of this length.
This brings us back to 4tph fast + locals threaded around them, a situation which worked reliably for many years on the current infrastructure, but with a capacity increase from 12 carriages per hour to 32+ between Leeds and Manchester. Local services can then be operated by stock which is suited to the platform lengths of the stations being served and the local nature of service (doors at 1/3rd etc).
That just leaves the smaller stations at the Eastern end. Scarborough works well as a shuttle so dont try and run through, Middlesborough probably wouldn't work as shuttle, but I think the only stations that might present problems are Yarm and Thornaby. A situation where two minor stations affect capacity across a major network isn't acceptable so solutions may not perfect. (travel in the front x coaches for Yarm and Thornaby) Forget about trying to carry on east from Middlesborough.
On the Hull route Selby and Brough already handle 9 car LNER 80x services without major problems.
Northwards from York to Newcastle all the major stops can handle 9 car 80x anyway, which just leaves Chester-le-Street, same comments as Yarm & Thornaby. Transpennine service shouldn't be running north of Newcastle.
This solution delivers enough capacity using the current infrastructure apart from platform length at Huddersfield, which should become a priority task to improve, even before 4 tracking east of Huddersfield, with possibly even a short term temporary solution while improvements are ongoing.
Order extra coaches for the 802s, to increase them to 8/9 coach units, order enough extra 8/9 car units to cover TPE north with 80x units. Two 4/5 car units are no good unless they are through gangwayed. Bin (pass on to anyone who will take them, they are a microfleet and just introduce operational difficulties) the Mk5 + 68s, and keep a few 185s to run the Scarborough shuttle together with a couple of 6/9 car 185s to act as reserve units to cover failures. Remainder of the 185s operate the stoppers on the Leeds Manchester route, and any left after that are deployed elsewhere if anyone wants them. Assuming TOCs remain York Scarborough might sit better with Northern.
When improvements between Dewsbury and Huddersfield are complete you then have a fleet which can take advantage of electrification and improved speeds, so you can look at improvements to journey times, building on a relaible base timetable and more local services if the demand is there.
This solution might not be the cheapest in the short term, but long term it would probably be better value for money. The reduction of TPE services to 4 tph fast also addresses another elephant in the room, staff shortages, TPE are still cancelling trains because of staff shortages. Fewer longer trains need less staff, and this also reduces costs as well. A more robust timetable means less delay repay and overtime when things go wrong, so again helps keep costs down. A standardised fleet reduces training requirements.
The next bit may be heresy but if you can deliver a reliable core timetable on the existing infrastructure do you want to spend the money on the Dewsbury - Huddersfield upgrade, or would you better going for the longer term proper high speed line across the Pennines and diverting the money into that. May be a bit late for that now, but this is a speculative thread.
Sorry if this post has wandered off topic, but I dont see how you can consider new stock on its own, it has be be tied in with a vision of whats needed to deliver a reliable and useful timetable. Its that vision which seems to be sorely lacking on todays railway, with each TOC working in its own silo, and working to support its own 'empire' with no intergration. Hopefully GBR will address the worst aspects, but we will see.