Well, it's really a pack of a few questions:
1) Are we attacking the petal or home island first?
I personally think taking the shot for the home island is worth it, circle our galleons around so they never see them coming and all that, but that's still up to a team decision really.
2) If we are attacking the home island, how well defended do we expect it to be?
We obviously see they have some defenses in their cities, like border cities on the petal. So, we have to ask ourselves -do we expect to see significant garrisons on the home island? If they have like 3 crossbowmen per city or something like that, we'd have to bring enough troops for serious siege - which would mean 5-6 catas probably, the usual amount to really take a city, given that once we land they'll probably immediately try to whip more troops and so on.
If we expect or at least gamble on catching them by surprise, so they just have a couple weaker units fortified in their cities, then we aim for our strike to immediately take cities, from amphibious landings even, so just go with maces/xbows and maybe a spear or two for cleanup garrison.
3) If we decide to attack the petal first, what forces do we bring.
Again, attacking the petal first isn't my preference, but if it is what we decide on, same question to ask. We have much shorter supply routes and would probably want to get some siege over there quicker though, would be my guess.