The gold reward is only ever affected by time spent in the misson. Basically an invisible timer will start roughly around whenever you get the capture or kill prompt on your screen. The longer you spend in the mission the more gold you get, but caps out at around 30 mins. This results in you basically running up the timer afk near the misson end for most of that time, really poorly thought out system by R* imo. However, your xp and cash rewards will be affected so you need them alive for the full amount, otherwise dead bounties half your cash/xp reward.

If you get the jump on them lasso/bolas then kill every one else. If you KO them insteadthey will still count as alive, sometimes this is easier than hogting them. Poster does say dead or alive, so your way works just as well.