Apply to Netjets Europe.
1500 hours is the min with 500 hours multipilot. You might have to get bits of paper from your company saying your King Air time's multicrew and if you haven't done so, do a MCC.
Do the type rating and do the LST. Voila, 1 full ATPL. Or, do the 500 hours on a multipilot type and then voila, ATPL.
Either way, the money's not bad and there's no charge for the type rating.
Got nothing to lose.
easyJet's recruiting for the hold pool at the moment.