An idea I've had in the past is having an hourly CrossCountry service starting / terminating at Leeds to give Leeds passengers more capacity without it being taken by York and Newcastle to Sheffield and south travellers; extending that to Hull probably wouldn't take up all of the space for those joining at Leeds. The problem is that I don't think there's enough space between Leeds and Birmingham (Bristol Parkway or anywhere else it might be useful) to currently run such a service.
Running the Edinburgh services via Doncaster in order to specifically release capacity for Leeds probably has some merit, but what really needs to happen is certain services having guaranteed longer trains.
There are 34 x 4 car 220s. This is perfectly reasonable, and with a good refurb, they will be fine.
There are 40 x 5 car 221s, and 4 x 4 car 221s. If someone had a bit of sense, we could move to having 20 x 6 car 221s, and 24 x 4 car 221s, which would really help as it would allow you to run some better-length single units, and also have loads of extra 4 car units sprinting about in 8 car formation, which is probably the longest they should be (9 cars don't seem to be accommodated at some stations).
Re-create 7 x 9 car 222s (this should wind people up), and then have a remaining 20 x 4 car 222s. When you consider that the 9 car 222s could be put onto a homogenous route, with First Class of a suitable size but perhaps the reintroduction of a proper, functioning buffet / cafe, you would be able to yield manage people accordingly. The 4 car units, e.g. 220/221/222 could have a limited First Class, and be refurbed more to suit things like trolley service.
With the full fleet in operation, you would be able to have a good switch around of the services.
Put Cardiff onto the 'Voyager' network full-time, and run those services as 6 cars onto the via-Doncaster route. As TPE and LNER need capacity north of York, you could divert this service to Hull via Goole or Selby, in line with the aspirations for a South TransPennine Hull; Hull being still served by express traffic over Huddersfield / Leeds, but this would be the 'new' Sheffield to Hull service.
Amend the Bristol to go to Nottingham, again probably using 6 cars. This would mean stations like Worcestershire Parkway actually get the sensible destination of Bristol for the wider South West, instead of needing a double change at Cheltenham. Amend the stopping pattern north of Birmingham so this one is only Tamworth, Burton, Derby and round to Notts.
Use the 9 car 222s on the Bournemouth to Manchester, so traffic to Birmingham Airport is on the longest possible trains. Diagram other 8 car operation in accordingly. You would have to have a timetable re-jig because of interworking at Piccadilly, but this would actually be a good thing as a delay in Bristol won't cancel a Bournemouth service.
Then overlay the second service (I'm sure the old pattern pre-Covid meant there were extra Southampton trains) with a Southampton / Reading to Liverpool, either via Solihull or Coventry (but if the latter, add in a Solihull stop, it's overdue), so that there is a 'proper' express to Liverpool every hour. This might have to stop at Hartford but that's no bad thing.
This would leave you using lovely 8 car 350s on something like a Birmingham International - Liverpool (every hour) and Manchester via Stoke / Macclesfield (every hour) to pick up the slack. I can't imagine people would be aggrieved at such a thing, especially if doing so would allow Congleton and Stone to go onto the route map.
I can already foresee some of the comments on this. "You can't get from Bristol to Manchester" even though quite frankly when you look at Birmingham's rail map, it makes far more sense for all South West traffic to go straight past University and up to the Derby lines, much the same by reply stuff from the South Coast just going to the North West. It also makes sense from a crew perspective - Manchester crew go to Reading, Derby crew go to Bristol. Having all these extra crew changes at New Street isn't helpful, just run 30-minutely paths across Birmingham and ask people to change.