So I bit the bullet (as they say) aaaaaaand:
No smoke These toys run happily on 2s lipos.
This is good news because:
(1) I can put out a PSA to the nerf community, as many nerfers who may be interested in the Laser Ops series will have lots of lipos lying about for their dart-shooting guns;
(2) I can get on with:
(2a) my arduino projects I had planned for these; and
(2b) designing an appropriate replacement battery tray to 3d print.
Thanks for your input guys, it's been fun.