Is it truly a "fairly limited period"?
I don't see the money required for major platform extensions being available any time soon.
Attempting to fit 400m platforms at Manchester and the like could cost a very large amount of money. From an inspection of the sectional and appendix and google maps, it appears to be that it would probably take a complete reconstruction of the station approach to be made truly workable.
A fleet of 275/300m trainsets, possibly with a handful of 400m sets mixed in, would seem to be the best option to get capacity out of the infrastructure that is known to be available.
We shouldn't bet the house on some future project occurring - indeed that is one of the reasons we are in this mess in the first place!
The point was that if the 10tph
3 to Birmingham will be able to be 400m
1 to Liverpool/Lancaster will need a 400m platform to split at anyway
1 to Liverpool which would see extra capacity from the above service (but could have a second unit attached to split at the same station as the above service to serve somewhere else, say, Blackpool)
3 to Manchester will give a small uplift over the day plus
1tph to Macclesfield which will relieve capacity a little in some of the above services on top of their existing small daily uplift
1tph to Glasgow which would see a small daily uplift although could see some capacity uplift by the Lancaster service being timed well to connect with TPE services to Scotland
Ignoring the Birmingham trains, that's 7tph, 6 of 8 coaches and one of 16 is 64 coaches of capacity, with the option of it rising to 72 (or even 80 if you could find a destination to split the Glasgow train as well) without needing to build any additional 400m platforms. If 6 of the trains were 10 coaches (to get to 11 might be an issue, as I believe that you'd no longer be able to serve Liverpool as it can't take 12 coach 390's) that would be 74 coaches.
That means to get nearly the same capacity out of London you'd only need to add the suggested Blackpool service to the Liverpool service, with more available if you could split the Glasgow service (especially if that was to Edinburgh where most of the same stations north of Wigan are going to be served, so it's only really once in Scotland there's a risk of people being on the wrong half).
If you can get a good interchange time on the Lancaster service (with the risk of wetting portion travel for this service and the Blackpool service being limited as the other half would be Liverpool, so whilst frustrating you're not heading a significant distance the wrong way even if you end up at the terminus) to a TPE service to Scotland you could move some 390's to TPE to slightly improve the journey time to Glasgow, which would take a few off the HS2 services to Scotland but still leave the direct services for those who need it.
However as soon as you are able to deliver 400m platforms for Manchester (as there's likely to be new platforms anyway soonish as part of NPR, or whatever it's called but definitely not HS2 into Manchester is why I said a fairly limited period) that's going to significantly boost the capacity into Manchester. One you've got the new platforms/lines to Manchester, even if the trains were limited to (say) 300m you would likely be able to extend the Macclesfield service, which would make it 4tph to Manchester (even if the latter only left 1 minute later than the previous Manchester service and arrived 1 minute before the following one, some people would use it if it wasn't as busy).
Other than Manchester, I'm not sure that anywhere else would benefit that much from 250m stock, even then Manchester would have 3 and a bit trains an hour (because of the Macclesfield service taking some of the strain) and have a small uplift over the day compared to the current capacity.
Therefore, what is the benefit you're getting from creating 10 coach trains and is it worth the cost, especially if you may need to run more 400m trains during their lifetime with the associated cost of reversing then back to 400m trains?
If you need to lengthen Liverpool to take 275m or longer trains, (as I believe that platform 9 is 267m long) then arguably it'll be better to use that money towards building the extra tracks into Manchester and the 400m platforms there as Liverpool is already benefiting from having 2tph and so the risk of those trains being the trains with capacity issues is likely to be small.
Given the above in yet to be convinced that there's a benefit from running 250m long trains, especially given you could always build some extra middle coaches at a future date to run (say) 300m trains to Manchester, or even build some new 4 coach units to pair up with the 8 coach units so you could run 300m trains to Manchester (or other places) but also split a 12 coach train to run to Liverpool but with the 4 coaches splitting to run separately into Lime Street (maybe as a stopping service or even just waiting at South Liverpool Parkway to then head south again).
Changing to 10 coach trains now is probably more risky than keeping the 8 coach units and setting what future developments happen (including where there's an actual need for extra capacity).