I think you can move over to the freighters, but you need medium jet, I believe, whatever the published minimums are for freighter, as pre-joining experience. Otherwise, you have to go the JFO route, which isn't a bad idea.
If you don't have command turboprop over 20,000 KGS, you need Airline Jet Transport, which I believe has a weight restriction of 40,000 KGS or something. Don't quote me, but I hope it helps.