I've used a Crown PCC-160 on a podium in a play, and it worked well enough -- but this was for light reinforcement with actors who could project.
I know boundary mics have been used on conference room tables for some time, but no idea how well they actually work.
It would certainly work as well as, perhaps better than, a lavalier element taped to the podium, but my gut feeling is that with either solution, in such a small room where the pastor doesn't have to project at all, background noise would make it far from ideal -- background noise from other people, moving air, etc. They'd also be sensitive to "handling noise"; it would take some trial and error to sufficiently isolate the mic from the podium. I used foam with good enough success in that play, but also there wasn't stuff like paper noise.
Is a move to a larger single room practical? I think the return on investment, and the scalability, would be much better there. In a room that seats one or two hundred, by the time you need an overflow room, you'd likely have some audio and video infrastructure in place, making the overflow feed much easier to do and better quality.