Whilst I applaud your travelling off the beaten tracks, sadly your chosen itineries look painful by train and then you'll need local buses/taxis. Whilst this is true of many courses a quick Google confirms my fears. Sadly the eastern side of England doesn't contain its best scenery, so the journeys may not seem as 'romantic' as envisioned.
A train to Sandwich or Deal would give you a lovely base and you could more easily access. RSG, RCPGC, Princes and North Foreland.
Then another train to the lovely Rye makes Rye and Littlestone accessible.
Purdiss Heath and Woodbridge are good suggestions but I hope never to spend another night in Ipswich. Aldeburgh is one of Britains most charming coastal towns and home to a tough, free draining links/heath hybrid. Both Purdiss Heath and Woodbrige are also top notch.
You do seem keen to see Royal Worlington. Both Bury St Edmunds and the smaller Thetford are good bases with the latter having a fine statue of Thomas Paine, who should be better known to Americans (at least based on the ones I've talked to
).
Alwoodley is close to Moortown and Sandmoor which have some reputation. Better to stay in Leeds and whilst I haven't been there in several years, the prospect of a return doesn't excite me.
I may be another trip entirely, but I'd throw Liverpool into the mix. It is a great and underated city with many fine links accessible by local train and short taxi rides.
Good luck and keep us appraised.