Well this is an interesting thread!
As a seasoned hunter with nearly 40 year experience, and six year of HFT under my belt I can honestly say that IMHO prone is the most stable position without exception. I can never find a peg when hunting though!
When hunting I sometimes revert to sitting FT stance if the grass is a little high though.
Regarding sitting when shooting HFT,I did once at Hull in about 2009 when having a complete mind blank, but Scooby called my bluff!!!
Different sports and different rules, just get on with it.