I just place the tip of my tongue on the roof of my mouth right behind my teeth and let it rest lightly there.
I've never had a problem swallowing with my tongue in that position. Doesn't sound like you're doing anything wrong. I'd suspect that if you just relax and let it happen you'll be OK. It might uncomfortable for you because it's different, but I'm betting that the discomfort and strangeness will pass in time.
Try and relax and let things unfold naturally. Keep us posted on how you're doing.
