Best way to buy 3 F tickets, as they’re more expensive compared to 3 individual F tix
 

You have not specified the air carrier, so this is simply a generalization. But, generally, all tickets in a PNR must be issued in the same fare basis. Thus, if there are only 2 "cheap" F tickets and you try to purchase 3, all 3 will price at the more expensive fare bucket.

There is rarely a reason to purchase tickets in the same PNR without status and especially flying in F. I would purchase each of the tickets separately. That way, the first 2 will be at the "cheap" F and you will pay the higher fare bucket only for the third ticket.

If you provide the air carrier, this can be confirmed.

That's it. Just buy them separately.

Buy them separately and after it is ticketed call the HA res line and have them "link" the PNRs. They will put a note in each record mentioning the other one(s) just in case something happens they know you are all traveling together just by looking at one PNR. I have done this several times with HA for the same reason the OP has.