Luckily, we haven’t (to my knowledge) had a “conflict” between two projects applying for the same funding when only one application/per organization is allowed. However, in cases where we become aware of this happening we try and go with a first-come, first-served approach.
One thought would be to combine the two proposals from the two different projects into one proposal coming from the fiscal sponsor. Maybe this is just being too tricky, but technically, perhaps it could work…