I think the problem is that the Hades as a lots of health to destroy. This means that at some point, the player is going to sit somewhere relatively safe and send missile after missile while calling support. Did someone found another strategy ?
On the other hand, if you try to send the player around to save GTA assets or anything else, chances are that the player will blow up. After 10 minutes or more playing, this would seriously piss the player off. And it is tough to have dialogues for 10 minutes.
I have not thought about how to solve this conondrum a lot. My general solution would be "much more easy provided you do a much more" : if the player is sitting somewhere, it is bound to fail, but provided the player react to new information, it could change a lot. The following suggestions are quick ideas, don't use all of them at the same time

Or use none.
Add "micro-events" like the arrival of the Orff, but sometimes tipping the game in favor of the players, sometimes in favor of the GTI. The members of the GTI infiltrated in the GTA would try everything to derail the operation : squadron of reinforcement turning against the GTA, some Fenris and Leviathan attacking the Orion (in exchange, limit the number of Zeus the Hades send). This way, the player has something else to do rather than shooting megabombs at the Hades. And taking the Zeus for quick response rather than heavier bombers would be a viable option (I took an Ursa). This way, the player would either choose the strategy "everything on the Hades" or the strategy "everything to protect what can send stuff to the Hades". You could even randomize the order of those events so for once the player does not count of his pre-knowledge of the mission to destroy the Leviathan the moment it jumps in.
Allow the player to choose when to call the Orff. Calling a Cruiser in reinforcement is damn funny, so the player would call it only when he has destroyed the beam on the side opposite to the Orion.
Make it impossible for the player to shoot from "inside" the structure of the Hades (lots of place to hide from the Lokis), for instance with an "EMP field" when the players get too close. In exchange, add some fighters on the player side, since he is going to be exposed a lot. (Actually, make the Alphas and Betas that can blow up repop).
When the Hades is at 10%, make it jump out, with a Red Alert mission in subspace. Of course, problem is that it would look like a little too much like the final of FS, so I don't know.
Last suggestion : right now the order of destroying stuff on the Hades is forced on the player : first the beams, then maybe the Weapon Syst, and then everything else. Maybe in the briefing give every "part" of the Hades a role, for instance : destroying communication would either stop reinforcement coming from outside or allow player reinforcements to come (once), Nav would destroy the EMP field I mentionned, some other place would allow the player to target the Lokis (before that, a strong jamming device hampers it), etc. Probably a little too tough to FRED.