The current system is the best one.
If you pay them an hourly rate, or just pay them a lump sum at the end, or anything like that, then they will not have an incentive to mark enough before the deadline.
If you pay them in accordance with how few people go for remarks, then they will be more likely to bump candidates grades if they were sitting just below a grade boundary.
If you pay them an hourly rate with the condition that they cannot mark anymore after a certain date (the deadline), there is no guarantee that their accuracy will improve, and there is no guarantee that they won't get lazy and mark less scripts.
Best just stick with what we've got.