I never went along with the request to leave Jesus out of a prayer when asked/allowed to do so during official proceedings - had many opportunities as a Senior NCO and Civilian supervisor. Would just precede using His name with, “And for those who believe in Jesus, I’ll close with this....others are just as free to pray what they prefer.”
I like your solution—I’ve done similar.
I told them no...you asked for a blessing and that's my reply.
Told them they could edit as they saw fit, but that was my reply.