I thought 'Ledbury' too, looking at that list, I really like Ledbury to browse around in (I was there last weekend, live not far from there) but in the name of being honest!:
WRT the well-connected bit: quite a few of the trains that are meant to go there and then on to Hereford get terminated at Malvern or Worcester, which is a pain, as they are infrequent enough as it is. However, that alone wouldn't put me off! As Ledbury has much to recommend it.
It's well supplied for independent shops, as well as Coop etc and a big Tesco, and there's Waitrose at both Malvern and Hereford. But the independent shops are amazing, and have everything you could need. The main street is really long, also lots of nice cafes (haven't been to the pubs there though). The big park that you'll see if you look on maps is private, but there is lovely countryside all around.
In terms of diversity, it isn't, nor are any of the southern parts of Worcs and all of Herefordshire, but my perception is that I would say 'welcoming of' (I'm white, so I can't speak from any kind of experience). Strong community feel, the Poetry Festival has a great reputation, lots of stuff going on. As it's between Stroud and Shrewsbury, if you are heading vaguely this way, it's worth a look.
Lots of people love it, but I couldn't warm to Stroud, and when I first left London a decade ago, that was where I intended to live. It is much busier that I thought it would be - the traffic through it really surprised me (at non rush-hour time of day). I think the villagey bits on the fringes are lovely, but the very central parts, the 'town' bit, I just didn't feel it was what I was looking for. The alternative, green, artsy side is very appealing, but I don't get that "yes, this is for me" feeling there. There are loads of threads on Stroud on Mumsnet, so if you do a search there's plenty of info.
If you are considering Frome, have you also thought about Bruton? It's become very posh, but it used to be on my list of 'that would be a nice place to live' ideas.
Sorry for the mini essay...