I suspect that Fyldes and Lowdens will be a bit more ringing than woody. If I could only remember what it is that PJ of PJ's music plays, I think that's the sound you are looking for. Any of the people he regularly deafens in sessions should be able to tell you - I think it's a Martin or a Gibson but it is not one of the usual suspects.

I have only heard good of Kinkades - but have never heard one up close and personal. Armstrongs are lovely but the body is usually a bit smaller and the sound probably less thumpy, but magnificent projection.

Max liked (and so do others) my Mugen THE-78 and careful hunting on ebay will get you one (or the identical Daion THE-78) for under £500, but they are more ringing than woody, although the bass is both big and long.

My late wife turned her nose up at an Atkin when I offered her one but it did have an interesting dark sound - probably OM sized.

An off-the-wall suggestion is Will Lancaster from Gravesend. He built Paul Steele a guitar that started life I think as a Martin kit but got modified - because Paul did not want to take his Zemaitus out to nasty rough places (and that Zemaitus stomped like a brontosaurus) and I haven't seen Paul out with the Z for years - he always plays the Lancaster.