A few years back, my obsession was cycling accidents rather than flying accidents, and there was pretty much the same problem. There are just over 100 deaths a year, versus 14 fatal accidents for GA.
At least for cyclists, it's almost impossible to infer anything from 'seriously injured' data, because this includes so much, from people rendered paraplegic to things that might spoil your day but which are not life changing. Rather a lot of 'seriously injured' people don't feel that they are 'seriously injured' enough to bother going to hospital, as an example.
You end up finding that your average cycling injury happens to a younger person (child, teenager) who is doing something dumb, but who probably gets away with a trip to A&E and no lasting harm. However, your average cycling fatality is an older person, possibly cycling to work after dark and often hit from behind - an almost vanishingly rare type of accident that is also exceedingly likely to prove fatal.
In the end I realised (as had some academic researchers) that fatal accidents were a much better proxy for 'life-changing' accidents, than 'serious' accidents were. I guess that's my bias coming to aviation statistics. But now you mention it, I can see it may have less justification in aviation.
On the other hand, the example you gave of a forced landing is one that may or may not affect both inexperienced and experienced pilots equally (somebody posted the other day that 80% were due to engine mismanagement) but where I would argue that experience would tend to swing things very much in your favour, all else being equal.
I wonder what proportion of forced landings do so little damage to the plane, that it's not notifiable as an accident? If it were a low proportion, one could search the NTSB database by type (e.g. C172, PA28) and chart the proportion of engine failures that were survived, by pilot hours. This might give some indication of how pilot experience affects manoeuvring skills.