Hi Brian ... I did a number of church name badges on FRP with the picture (or rather a pen and ink line drawing of it) and then applied a label from my brother machine for them to do exactly what you suggested.
On some name badges for 'key' people in the church we just engraved their names.

I have attached a picture of it.

How about if the people pay for their own badges? Cuts the cost by 100% for the church and you still get all the business. A win for both!

Gary