Are you using just the tips of your fingers @megs? Have you tried the sides of each finger, or even the nailbed – I think @Tim stabs himself there, so hopefully he can add his wisdom on that.
Is it definintely a skin thickness issue and not a blood flow issue? I find a bit of arm swinging before doing a blood test makes me look like an idiot, but does improve the blood flow to my fingers. Or running them under warm water helps too. Do you think that would help?