Where to stay? Cumbria Coastal Towns

There is engineering work on the line on all days from 30 August to 21 September to drain old mine water from Bransty Tunnel at Whitehaven.

Trains will be replaced by buses between Sellafield and Workington, with some revised rail timings.

On Saturdays to 12 September the bus replacements will start back from Millom, and on Sundays from Barrow.

On the weekend dates the buses are unable to serve Ravenglass station due to bridge heights. They will instead serve Muncaster Castle.
Other non served stations will be Kirkby in Furness (stops on the main road), possibly Bootle, Parton (stops on the main road), Nethertown and Braystones (taxi only, due to narrow roads).

It is going to be good fun.

For Roman ruins and Muncaster Castle it has to be Ravenglass. It is a small village, not a town. But you want to at least make that a stop on your way north.
Muncaster Castle is about 30 minutes walk from Ravenglass station via the Roman ruins at Walls and through the woods. Forget taxis and ubers. A taxi would have to be ordered from Gosforth, Seascale or Sims Motors at Eskdale.

You can actually stay in estate property at Muncaster Castle , otherwise the Pennington Arms at Ravenglass.

St Bees is a decent sized village with good walking and the Priory Church. You could even walk the coastal way from there to Whitehaven in a fairly relaxed 3 hours. It is the obvious choice.

Maryport has the important Senhouse Roman Museum. The town is trying very hard to reinvent itself, and does have a good harbour and marina. Very limited accommodation.
If you stayed in Maryport- the Waverley Hotel is the one good choice I can think of- next day take the coastal bus up to Silloth, thence Wigton to join a train.

I'm not sure why you are missing out Whitehaven with it's museums, harbour and Georgian St James' Church.

The buses are also unable to serve Whitehaven station due to bad parking, so will be using public bus stops just down the street.

Are you particularly wedded to heading north up the Cumbrian coast? The quickest train routes to York would be heading south, either back through Manchester or more interestingly changing at Carnforth and Leeds. You may already have covered this direction or may have good reason to head north but if not you could look at Grange-over-Sands or Arnside as possible coastal places to stay a night. Unfortunately the option to make a once in a lifetime guided walk across the otherwise treacherous sands between the two isn't available in September - the last walk is on Sunday 31st August. But they are lovely small places to spend a night and Arnside would allow some fine walking in the Arnside & Silverdale National Landscape.https://www.arnside-silverdale.org.uk/discover

Thank you so much for the thoughtful replies! I won't be doing this trip till the 24th of September, maybe there will be new challenges for trains and buses then... it all looks so easy on paper.
I think Ravenglass looks the best. I would love to visit Grange over Sands, and the Morecambe area, but decided to take the train north just to be on the coast while I'm in the area.
Thanks again!

Every one will be very disappointed if the line is not re-opened on time, as the closure has been being planned like a military operation for months.
Unless something truly unexpected is found there shouldn't be a problem.
The taxi numbers you might need are-
Gosforth Taxis - 019467 25308
Eskdale Taxis (Sims) 019467 23227

Do get one of them to run you up to Hardknott Roman Fort. Given a choice my option would be Eskdale Taxis.

Ravenglass was the end of a chain of coastal fortifications which continued from the end of Hadrians Wall, and also a naval base. A Roman road then ran East to Ambleside (whose fort you will have seen earlier in the trip) and beyond.
The dramatically located Hardknott Fort was on that road, a key fortification.
So not something you want to miss.
Some of the stones from Ravenglass Fort were "robbed" to help build Muncaster Castle, and others to build Muncaster Church (usually open 24/7)

UPDATE - Preparatory work for the closure of Bransty Tunnel took place last weekend.
That found problems regarding the condition of the ground for the heavy plant which will be needed, which requires remedial work to be designed and undertaken.
The tunnel is now closed until further notice. Locally a date of 1 November is being floated.
Buses are now in place between Sellafield and Workington.
The service between Barrow and Sellafield is heavily amended and reduced. Between Workington and Carlisle some services are retimed.
This is a fast developing situation, the above is all that is known currently.

This has a heavy impact on the locals, and the tourist trade.

That does change things a bit! I do really appreciate the information about changes on the trains. I just finished listening to Bill Bryson's Notes from a Small Island, and the idea of the Settle to Carlisle rail sounds really interesting. Thanks again for the help!

Yes the Settle and Carlisle line would be a good option.
If you are starting from Barrow (I'm pleased if you are, as the Furness Peninsula is way under-rated on here) then it's a 4 train job.
Barrow to Lancaster, Lancaster to Carlisle, Carlisle to Leeds, Leeds to York.
For best value you would book that as 4 separate Advance Tickets.
Well worth the ride.

For ease I would usually go Barrow to Preston, Preston to York - scenic in it's own way but far less so than the S and C.
You would book that as two separate Advance Tickets.