I need to get this done, likely this weekend. What’s the best way of doing this? Is there a quick way of getting it done, or should I resign myself to scraping the old cement off and laying them all down again on a bed of fresh stuff?

Chip off old cement as best you can, put a fresh bed down and re-lay them. Don’t do the five dabs of mortar, one in each corner and one in the centre though. Wet the slabs first so that they don’t draw out all the moisture in the mortar.