I'd personally lean even more into the fact it is a long range support hybrid ship, if I were to change the Gemini.
Given the Gemini has only 1 bay, it eliminates it from the running in fighter spam scenarios. The existence of Converted Hangar Bay means any destroyer can have a similar, if not quite as strong, fighter contingent. Certainly an Enforcer with converted hangar bay and a Xyphos wing still has 73 OP left (compared to a Gemini and Xyphos with 57 OP left), and is a much stronger base chassis than the Gemini, for the same deployment cost.
As for the hybrid nature of the ship, I think Alex is moving towards simply having ships be worth their deployment cost, which is the way the Venture went, and the Apogee is currently sitting at (or beyond depending on who you talk to). Right now, the Venture is more of a cargo ship than the Gemini is (14 DP and 3 fuel/ly for 600 cargo and 180 fuel, versus 9 DP and 2 fuel/ly for 250 cargo and 70 fuel). Which is consistent with the removal of the civilian tag. Venture feels worth while dropping into battle at 14 DP, at least for short ones where it's missiles don't run out.
So if I were to try tweaking a Gemini into a 9 DP tier destroyer hull, I'd probably try the following:
1) It's weapon count is pretty low for a destroyer. I'd add 2 small composite mounts on the front of the saucer section, roughly parallel with the missile mount, with 180 degree arcs, pointing 45 degrees away from forward. I'd add 10 more OP because 2 more small mounts were added.
This provides flexibility to put point defense either in the smalls or mediums. Since the Gemini's armor is so low, it's in danger of going down to an interceptor strike. If you don't put Mining Pods or Xyphos in the fighter bay, it can't rely on it's fighters for PD either, so simply more mounts that allow for different PD solutions seems good. It adds swarmers and vulcans to the already possible double flak.
Alternatively, a medium and two small missiles makes it reasonable to throw expanded missile racks on, and utilize missile pressure to keep flanking frigates away.
2) Bump the flux dissipation up to 200 from 170, to also help the fact it has 2 more mounts. Bump flux capacity up to 3200. That puts it roughly at 80% of a Hammerhead's flux stats, and about on par with an Enforcer (which is a low tech ship compared to the Gemini's midline doctrine).
3) Bump the speed to 60. It's not going to win any races, but at least it can keep up with things like Eagles and Champions and perhaps be set to escort on them, making it a reasonable midline support addition. Trying to get a slow carrier to escort a speedy cruiser can be painful to watch.
So, 85 OP, 1 Medium Missile, 2 Medium Ballistics, 2 small composites, 1 fighter bay. 200 flux dissipation, 3200 flux capacity shield, 250 armor, 4500 hull, 60 speed. The same 250 cargo/70 fuel capacity.
It is more on the glass cannon end of things, but supported properly can dish out destroyer tier damage, and between fighters, missiles and ballistics, can imagine a variety of viable loadouts. Although, obviously would need some testing, as I could be underestimating those changes. But certainly I want it to be able to, say, take on a non-SO Shrike.