Yes, don't bother with a BSA springer. Not even close to a HW/TX.

I've also owned a Venom HW80 Lazaglide which was a beauty and so smooth.

FWIW, the standard TX200 was the most stable gun on aim of any I have used. The HC version is shorter and lighter and the lack of muzzle weight makes it a little less rock solid standing. With the TX guns the stock is a little deeper in the fore end than the HWs, unless the 97 has a deeper stock than I remember, which means much better handling when shooting off your knee with a padded glove. This is how I shoot when using hides (with backrest) and so I found the TX200 nicer to shoot in this way than the HW80 Lazaglide. It just sat at the right elevation because the base of the stock is pretty well level with the bottom of the trigger guard.

Its a shame Air Arms do not make TX200s in .20, as with 11.5grain H&N FTT you'd really have the perfect hunting springer! I love the calibre.

The other option might be a used Theoben Gas Ram. Again, I'd avoid .177 in such guns and stick to .22, .20 because they operate under lower load and shoot with less 'snap'. I once had a scirocco 2000 in .177. Whilst deadly accurate, it really did have very snappy (but quick) recoil and just felt harsh. I believe they no longer make the ultra carbines in .177 for this reason, but might be mistaken.