1. One Round On / One Round Off: Have one round with this system, then one with the old, and so on.
2. Two Rounds: Running at same time, one old, one new.
3. Smaller Families: I say 5 man families all the way guys, I mean it would create like 5 or 6 new families and with a more target rich environment the morale wont matter as much. That by increasing the number of families you increase the number of targets, rather than just 2 top families their might be 4, rather than 3 mid level families their might be 6, there is always going to be someone to hit and would make it a lot harder to NAP half the galaxy.
4. One NAP Rounds: Just bugger off NAPS just allow 1 NAP per round then really no one should complain they have no targets. Does not stop you messing the leader and arranging a mutual "cease fire" but always leaves the option of war as well. That may however cause to many people to "Turtle" rather than jump for spread, still can't complain about lack of targets.
5. You Attack Me I Attack You: I think this out of everything is my favourite option because to me it makes sense. Okay if I was a "Big Nation" then sure if I attack a really small nation for no reason then my people will get upset, it will cost me huge morale, fair enough I get that. IF HOWEVER that small nation attacks me first, then game on beeeeeach.
That yeah okay Mr small attacker if you don't attack me I can hardly touch you, however if you do attack me then my morale cost to hit you back do lower dramatically. I mean what was wrong with that? Hey my people didn't want war, they didn't want to attack you, but hey you attacked us first now my people are painting smiley faces on missiles 
6. Faster Morale Gain: Maybe a system where you get a faster morale gain depending on the number of planets you have, that would mean it will still cost a big player a ton of morale to attack smaller ones but you could attack a few more times. Like as it stands a small enough attacker can attack you 100 times and you can do 1 retake a day, 2 if your lucky. If you got a slightly higher morale regain for been bigger maybe you could at least do say 10 or 15 retakes at least, even it out a little.
7. Morale Op: To complicated (I Know) but I have always loved the idea of a healer like operations in IC, things that you can cast specifically on family members only. Boost speed / increase armour / shield fleet / but sure one of them at least could me boost morale so that bankers sat around with little to do could at least ramp their attackers morale gain.
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Think my conclusion overall is that if people did want to turn IC around then it would take far far more than just changes in morale, that the game needs advertising better, better training available, videos teaching people how to play IC.
But personally I'd just opt to redo the entire game.
Whilst some people would say this style of game is dead, its all xboxs and high graphic games now I still believe there is a solid future for tick based strategy games, that if redone on a more modern level it could again grow.
For many years people have said what they want from IC and most of the time those voices "Now Gone" have cried for new units / new ops / new buildings / new tech options / better chat / varied galaxies / new races.
Perhaps another idea would be to have "Faction Wars"
That if the mods could place the starting worlds of families then that would be kind of great. I would assume they simply picked where a home world would be but not actually know which family would get allocated that slot.
In which case you put 4 families on one side and 4 on the other side and have 4 v 4 with no morale or seriously reduced, rather than having to pick targets its simply "them 4 families over there need to die" think it would be fun to try that.
Why not have some kind of team galaxy like that as well.
In SN it matters how you play
In SB it matters how your family play
In ?? said faction galaxy it matters how the families your faction play
No you wouldn't need have a random family as player numbers in the 8 or 10 families could be increased / decreased to fit player numbers. 5 a side sounds good to me, you should get 2 decent fams, 2 moderate fams, and 1 smeg fam on each side.
If I could change one thing however it probably would be smaller family sizes, I'd rather play alongside 4 or 5 other players and have 15 families to fight than play with 9 players and have 8 families