What if we made a little list, of the Enterprise-F and other hero ships (active canon ships, some STOnly C-store models, maybe tribute ships (think a Bellerophon named U.S.S. Hawking) or easteregg ones (U.S.S. Protector, captain Allen commanding)), and add a small chance (somewhere between 0.1 and 1 % - though maybe that's too small) of one of these named ships responding when you use Fleet Support?
It'd be much like the appearances of the Enterprise and the Wells class in Tau Dewa missions, with a little flash dialogue upon arriving and departing, and either doing the repair-thing or warping out instead of exploding when 'destroyed'. (Can't have some random Klink blowing Va'kel Shon out of the stars in the a PvP map. A strategic retreat would be ever so slightly preferable.)