What about a Medi Gun that takes inspiration from the outdated medical practice of using leeches to transfer blood? Something like:

(=) Transfers health between Medic and heal target to ensure their health bars match
(+) 50% of damage dealt by heal target is returned as health, which can overheal
(+) damage received while healing is transferred to heal target based on ÜberCharge percentage
(-) Medi-beam cannot overheal
(-) 25% slower heal rate
ÜberCharge triples life leech effect and health transfer speed