I really think Wasps should be one bigger tender, with no guns or perhaps just a single PD Laser, that controls 6 drones with moderate roam radius and slow regen, personally.
What you describe isn't that much different from a Shepherd. If fighters can use ship systems, you could try implementing a 2 fighter wing with drones and get more or less the same thing, though given that fighters and drones appear to be roughly the same size (especially Wasps and drones), I would tend to find a fighter-sized drone tender to be a bit out of place.
Considering staggering pilots losses from fighters usage - pilots better be cheap than standard crew. Some clones or robots or something else to pilot fightercraft. Using wasp wings will drain crew very quickly - too bad old system with drones was scrapped towards crew for all fighter types. Crew for constantly destroyed fighter craft makes no sense as it is effectively prohibits fighter usage because of big crew losses. And this doesnt explain how crew from destroyed fighter teleports into new repaired at carrier fighter. I say remake fighter craft into experience-less drone craft with carrier experience affecting performance of launched drones.
1. Green crew is already dirt cheap, and I don't think that crew experience matters that much for fighters except in determining the number of replacement craft.
2. In my experience, the crew losses are not significantly more serious than a primarily frigate or frigate/destroyer fleet would suffer, though this could be down to fighter/ship choices and luck. I feel that you're exaggerating the degree to which the crew losses make fighter usage prohibitively expensive. Each fighter lost is maybe one or two crewmen lost, tops, and you only get (fighter wing's CR rating)/(per-fighter CR cost to deploy) fighters in each fight, so the absolute worst you can do if you lose an entire fighter wing is something like 40 crew (Piranha or Gladius Wing, 100% CR); if you're looking at more normal CR values, then the maximum possible crew loss is more like that of a frigate or a lightly-crewed destroyer, and all this is assuming that that bug that made it so that excess crew wasn't hurt by ship losses is no longer in effect; if that bug is still in effect, then fighters might be unable to cost you more than maybe 6 crew per battle even if the entire wing goes down.
3. There's nothing that says that pilots from destroyed fighters teleport to the carriers to pilot the next fighter that launches. Carriers tend to have plenty of crew capacity, and presumably one of the people over the minimum complement gets shoved into the next available fighter. If you're running minimum crew levels, well, it's not like the game seems to track crew levels during the battle, anyways; even if your Medusa goes down to 1% health, it still has its start-of-battle combat readiness (less whatever CR it lost due to deployment time), if I'm not mistaken, which indicates that as far as the game is concerned the Medusa is still as fully crewed by as elite a crew as it was at the start of the fight, even if after the battle you discover that you lost all 30 of your elite crewmen and that Medusa was the only ship that took any damage.