I went to the Great Western Museum in Swindon last September. Basically, you have part of the old locomotive works turned into a museum. Nothing is in steam. The National Railway Museum in York is much better. Just west of the GWR museum is another part of the old works - turned into an outlet mall. The GWR mainline to south Wales is being electrified.
2 years ago, I went on the Snowdon Mountain Railway. Note that demand is high and places limited. If the weather is poor, you will end up in the clouds. I went up in perfect weather & took pot luck & just managed to get a seat. The building just below the summit offers protection in the event of bad weather. The ride is well worth it. Note that you pay extra if you want a steam locomotive and the vintage carriage does not have opening windows. It looks like the diesel pushed carriages do have opening windows = best for photos.
On day 10, you should be able to also throw in Dyrham Park (NT) - but see Castle Combe first. (Roads between Bath & Castle Combe are narrow. Follow route on Google Earth to get familiar with it).
On day 11, I would delete Caerphilly Castle as you are going too far out of your way - and the M4 around Newport frequently jams up. Instead, leave Thornbury and take B4461 to cross the Severn (toll) Bridge and go into Chepstow. Park in car park by castle and walk around the corner onto the bridge over the Wye for a good view of the castle. (It also work taking a photo of this bridge as it is one of the World’s oldest iron bridges). When you leave Chepstow Castle car park, go into the one way system along narrow streets. It would pay to look at the roads on Google Earth as to how you get to the A466 for Tintern - as it is confusing.
On Day 11, after Tintern (delete Caerphilly), you are heading for Hawarden for the Gladstone Library. So, it sounds like you are into steam engines & books? The quickest way to go would be A466 to Monmouth > A40 eastbound for about 4 miles and then left onto A4137 to eventually join A49 for Hereford. Now, Hereford can be pretty congested but you might like to make a stop to see Hereford Cathedral.https://www.herefordcathedral.org
Going north up the A49, it is well worth calling in at Ludlow = real Ye Olde England! www.ludlow.org
Just north of Ludlow on the A49 is >
http://www.english-heritage.org.uk/visit/places/stokesay-castle/
Shrewsbury is also of interest - use the Park & Ride if you wish to visit.
Proceed north on A5 & A483 though may like to make a slight detour to see the Pontcysyllte Aqueduct. The area around Hawarden is not very interesting and a bit industrial.
An alternative to the above is to go from Monmouth via Midlands (M50 & M5) & see:> http://www.svr.co.uk on way to Crewe.
Another alternative to the above is to go from Monmouth west on the A40 to Abergavenny and then via Crickhowell for A479 and A470 which will take you through the scenic heart of Wales direct to Snowdonia*. (This would be my choice and I would stay in NW Wales on the nights of Day 11 & 12. (Your plan has too much travelling from Crewe to Snowdonia). When you stay with friends in Crewe, that is when I would visit the Gladstone Library and I would combine that with historic Chester - which is virtually on the doorstep.
* You may be interested in going to Aberystwyth for an overnight and see:> https://www.llgc.org.uk
& www.rheidolrailway.co.uk
If you buy a ticket from Crewe to York, it will cost you £46.20 - whether you pay on the day or advance book. Do this:> Advance book (about 10 weeks ahead) CRE > MANchester - which can be as low as £3. Then pre-book MAN > YRK - which can be as low as £10.50. Note that this is for specific trains - so make sure you match up the timings for the change of train at Manchester Piccadilly. Be sure to also pre book YRK > KGX & PAD > SWI.