2 layer board design and grounding
You should really start off any two layer design with the intention that the bottom side is reserved for ground and that the ground plane might occasionally need to be interrupted (now and then and minimally) by signal and power tracks that need to cross each other. It sounds to me that you may not have started with this sensible intention/philosophy.
If it means ripping up and starting from an earlier point then this is likely to be better in the long run (all things considered) in my opinion. As for the thermal pad what's wrong with placing a number of vias like this: -

If they need to be a tad smaller than the other vias, that shouldn't be a cause for concern.