If your goal is to get the cheapest possible flight then separate tickets is definitely the way to go. If there are not enough cheap seat when you purchase initially them you get charged more for some seats.

Alternatively, if you are checking in at T-24 (exactly) you can (depending out your hardware and resources) either open multiple sessions or multiple different browsers and trigger the check-ins at the same time. You could even delegate the responsibility for checking in at T-24 to the other passengers. You could even organize a group check-in with a countdown.

I haven't faced that scenario in years, although my A-List Preferred wife and I (a mere A-List) get somewhat boarding positions, so far we've not had to separate, although occasionally her preferred seats (the LUV seats) are taken. I don't care as long as I get an aisle.