Tigerair have recruited people just like you (i.e. permanent residency status pilots) over the past year or so. And yes, for the RHS.
Keep looking at their website (and all the other companies for that matter) regularly to see when they start to recruit again.
This link takes you straight to the TGW page;
Tigerair
As for being able to speak to HR/chief pilots of companies of the kind you are wanting to work for - nowadays in this country it's pretty hard to get that 'personal' touch.
Good luck though.