Sign up bonuses are definitely the way to go given your time constraints. But it’s not obvious to me that transferring points to miles is actually a great strategy in your case, unless your goal is to get one or two business class tickets (using miles) and then pay cash for the other 4-5 people in your party to sit in economy.

With a “premium” card Citi, AmEx, and Chase points can be redeemed for 1.25-1.54 cents/pt for airfare. It would be difficult to beat that exchange rate by redeeming miles for economy tickets, unless you have to buy tickets last minute. If you want to redeem for business class travel then exchanging for miles is generally the way to go (though not always — there are some absurdly cheap business class tickets on Chinese carriers ex-LAX these days!). But the chance of finding 6 business class award seats simultaneously available on one flight is effectively zero, plus you’d never save enough for 6 tickets in less than a year anyway.