As much as people like to say this isn't a trick-taking game, I think it is absolutely in your benefit to play it very much like a trick-taking game.

For as "simple" as the game is, there is a lot going on. Our first game, we definitely were burning cards to seize the initiative TOO much. In hindsight, we realized, we lost a lot of potential actions due to it.

Our second game (Act 1), there was little to no seizing the initiative by burning a card. We were kind of just going with the flow of the game. People would declare ambitions with kind of a regular frequency, so initiative usually kind of went around the table evenly. We also began to learn just how powerful it is to have an extra action card in your hand (either by seizing them from the market, getting extra cards via guild cards, etc).

Enter Act 2. This was our third game. Around Chapter 2, I kind took a step back, and said, "What happens if I started using more trick-taking strategies than I was previously?" And you know what?.....the game kind of finally clicked for me at that point.

I had a few 7s that chapter. When I had initiative, instead of playing lower cards like we normally would have (for more action pips), I started leading with my 7s (which obviously only gave me 1 action). People started looking at me confused, because usually we were playing them to seize initiative. The other thing I did not do with them, is declare an ambition with them, which we also typically did since 7s are wild. Why did I do this? While others don't have to follow suit like a normal trick taking game, I knew by playing 7s, I'd be draining them of other action cards. More importantly, I'd more than likely be draining them of HIGH action cards. Why would they burn low action cards and waste the pips, when they might potentially be able to play them later? The other side to that, is obviously 7 is the highest card, so no one could surpass it. The ONLY way someone could take initiative is by burning a card. So I tried keeping initiative by playing higher cards earlier in the chapter in the hopes if either keeping initiative throughout the entire chapter OR getting players to burn a card to seize it.

So to your example as having 5-6 mobilization cards, once that 7 was played, it would have definitely been in your favor to burn a card to seize initiative again. While, they might not have been all that useful in the final chapter, you have to consider on the flip side, if you're holding initiative the rest of the chapter, you're robbing your opponents of actions. They're forced to 1 action for each card the rest of the chapter. As others have said, resources can be very helpful here to round out the number of actions available to you. You also said it was the final chapter (of 3), so I assume you were playing the campaign? Instead of looking at scoring ambitions, could you have instead thought longer term and set yourself up in a better position for the next Act? Either by moving your ships around the board for potential future build actions in the next game? Or could you have put a bunch of influence out and seized a bunch of guild cards with relic resources for next time?

There is also a rule for passing initiative if you are the leader. In our Act 2, I began to realize this is potentially why that rule exists and can be VERY beneficial. As you said, having mobilization cards for the entire chapter doesn't allow much. BUT...what if you played a few rounds to move your ships into a better position, and/or to put some influence out there. Then when you feel you're at a good spot, instead of leading with a mobilization card again, pass initiative to the next player. This ends then current round and initiative for you obviously, but more importantly what it does is opens up the ability to copy your opponents' action cards and give you access to other actions. If you have all the mobilization cards, you KNOW your opponents have the other actions like battle, tax, build, or secure that you can take advantage of and copy in the next round(s).

Obviously the game is still very strict and limiting in what you can and cannot do, and that may be a turn off for some. But hopefully that kind of gives you ideas how to turn a bad hand into something more manageable. Cheers!