..the question becomes how one addresses the 'gap' in terms of experience of emergencies....
Might the answer be to encourage airline pilots to engage in the kind of flying which engenders emergencies?
I'm a humble glider pilot, like the OP, but in a mere 400 or so hours of flying I've experienced at least 2 potentially life-threatening situations which required me to sort them out to survive (plus maybe 50+ as training exercises with an instructor on board). I'd imagine microlighting is equally exciting, as would be mountain flying, floatplane flying, and paragliding/motoring.
I understand that some airlines disapprove of recreational flying, or at least count it against maximum flying time, which seems potentially counter-productive.
[PS the "at least 2" phrase is because in gliding some things are quite standard - thus I don't count avoiding a collision by 500ft or landing in a field, which might well be potentially life-threatening in other forms of flying. If those go in, I've survived dozens of times.
If anyone's interested, the two were:
Canopy opens on a winch launch, with potential for spinning in or the canopy flying off and hitting control surfaces - solution, use elbow both to hold down canopy and to manipulate some flight controls for landing.
Aircraft (new type) fails to recover from spin - solution, work out likely cause (rudder overbalance) and redo recovery actions properly.
Both rather non-events really.]