That's not very easy to do, as they'll be portion-worked with a Liverpool-Llandudno service. (I presume you don't want to start shunting coaches at Chester on an hourly basis.)
I did not realise that both services would join to go to Liverpool as I thought they were separate services.
But then Manchester would loose some or all of its through services to Southern England.
Run them through with a 67 on the front if through services are considered to be essential. Such services from the likes of Liverpool are already deemed to be unnecessary.
I don't know exactly how many passengers travel through Birmingham but when I went from Cheltenham to Stoke around 20-25 people stayed on just in the carriage I was in. Don't forget it is not just Manchester to the south journeys but also those from Wolverhampton, Stafford, Stoke as well as other places.
Like I said, they'd be used to strengthen other services that are chronically overcrowded.
This may be a terrible idea but a way to solve platform capacity could be to have the service those 2 services joined up to run Bristol, Birmingham, Reading, Bournemouth. No one would use it as a through journey but it may free up platforms at new street but I have not checked the timings.
Run it with a 67 throughout
If TfW were to get any more than the 3 sets of mark 4s currently planned then I would suggest using the additional sets on Swansea-Manchester services (in 5-car rakes), rather than making any more of the Holyhead-Cardiff runs LHCS. Through services between Cardiff and Carmarthen would be maintained by introducing new DMU-operated services via the Swansea District Line.
Or potentially by extending this open access Bristol - Swansea service that's been applied for.
This is all hypothetical anyway as I'm not aware of any plans for TfW to get more than the initial 3 mark 4 rakes. But if they did get any additional mark 4 rakes then in my opinion they should be in 5-car formations (or more if the demand requires it) and used on Swansea-Manchester, whether that would be all services on the route depends on how many (hypothetical) additional mark 4 rakes we are talking about. If enough mark 4 rakes were available to cover all Swansea-Manchesters plus the 3 per day Holyhead-Cardiff then yes, that's what I think would be the best thing to do with them on the franchise.
I like the sound of a faster Carmarthen to Cardiff service but are there many through passengers from West of Swansea who go past Cardiff?
I've got no hard facts to go on there but my gut feel is that Cardiff seems to be one of the big draws. Possibly some go to Newport, but I doubt many pepole from Llanelli and points west stay on the Manchesters beyond there (some do of course, but I doubt having to change would put many of them off). Why? Because once you start heading north again going via Cardiff starts to become quite a big detour and rail less and less competitive (particularly since the current service goes via Swansea which means even getting from Carmarthen to Cardiff is sadly slower than driving at present). Apart perhaps from passengers to Newport, most passengers going beyond Cardiff from S.W.Wales will probably be changing there anyway onto London/Bristol/Cheltenham services. With Swansea-Manchester, the starting point is a bit further south than Carmarthen so going via Cardiff is much less of a detour than Carmarthen-Manchester (if you wanted a train to do that your best bet would be going back in time and pleading to keep the line to Llandelio open).
Ideally if you were going to do it you'd have planned it in advance and ordered less new DMUs, but at the very least freeing up the 3-car units that are planned for Swansea-Manchester to instead be used on the Cambrian (minus first class which apparently won't be fitted when they are first delivered anyway) would be no bad thing.
There are four documented users, only one (GU Cardiff) is proposing full length, and the other three (TfW, Alliance Blackpool and LNER Edinburgh) are all proposing short forms.
I see your point but I'm concerned that large numbers of new DMUs would create a serious dent in rail's environmental credentials. There is now a (non-binding?) net zero emmisions target for 2050, and to keep warming below 1.5 degrees that probably needs to be sooner. Given a 30 year life, today's new DMUs would still be running in 2050. Replacing trains more often than necessary (eg. a 15 year life rather than 30) also has implications due to the energy use / 'embodied carbon' of building the new fleet.