I don't know if you will find availability from RSW, but you have enough miles to do what you want to do, just barely, if you can find award space.

Basically, you need 10 one-way awards, and you need them grouped as a 3, 3, 2, and 2.

Forget about BA. It is good for coach to HI in some cases, but it treats AA or AS first class as a first class award and thus requires 3x miles. Instead, convert 120k Amex to SQ. SQ lets you book one ways on star alliance, and domestic US first prices at the business level on SQ's chart on a two-class airplane. (I am not 100 percent certain this holds for trips to HI but I am pretty sure.). You cannot use your SQ miles for unlimited numbers of friends and family -- each person gets 5 nominees, but that's plenty. Or you can just send 30k to 4 different people instead of all 120k to one. Same difference. Any way, here's how you put the jigsaw puzzle together with what you have:

120k UA gets 3 of you one way in F -- on UA or US or a combination of the two. 75k AA gets two of you one way in F -- on AA, AS, HA or a combination of the three. So, that gets all five of you there (or back) in F.

Now coming back, use 40k UA for one of you on UA or US in F. Use 30k SQ to get a second person in F on that same flight. Use the remaining 90k of SQ for the last 3.

Caveats: I am dubious you will find enough seats at the saver F level on US or UA to make this happen, but this is the blue print for how to use your existing miles. Note that Amex does not transfer instantly to SQ. This can lead to some nervous times if you are watching award space while waiting for the transfer.