...just thought of another.... the Brocock Atomic.
Another suggestion that I had never come across before! I have to admit though after having had a ramble round the web I stumbled on a massive thread all about the PP800 on the other forum. The apparent ease with which they can be worked on and tweaked does appeal. None of the rifles I own or the HW40 went very long before they were disassembled into their constituent parts for a poke around so another pistol which is ripe for a bit of garage time would be an added bonus in my eyes. The inletting on the grip looks relatively straightforward as well so the clunky wood work could be improved or replaced. Better get saving!
Be good. And if you can't be good, be good at being bad.
Aeron-Brno B96 and B98 are another, though scarce, option.
Bit of a curve ball, but how about the Umarex S&W 586? Apart from it not being PCP, it seems to tick all your other boxes - self indexing, adjustable sights and a reasonable trigger.
I am not a great fan about the looks, but I have great fun shooting with mine - especially with the 0.22 9.5 inch barrel fitted.
Too many guns, or not enough time?
I don't know of anything you could get for 200-300 quid which ticks all your boxes.
I have a HW44 which is (I think) the ultimate plinker but it's not semi auto and you said it's too pricey.
I also have a Steyr EVO10 which is great again but again not multi shot and out of budget.
I would just stick with the usual CO2 plinkers or raise the budget and go for the Steyr you mentioned.
Lewis