The membership system has been upgraded and it looks like I'll be able to engineer it so that everyone can take bookings directly via their Events Listing.
There is a working example of this here: https://integraleyemovementtherapy.com/event-list/#!event/2020/8/6/4-days-of-iemt-training-with-andrew-t-austin-in-rochester-new-york-usa
Click on the Register Now button to see the options appear. The system integrates with either Stripe for card payments, or Paypal, but at this time cannot integrate both on any single listing. It has decent flexibility in that you can put in the timings of when the price changes for early bird discounting etc, so that it changes automatically on the selected date.
Please let me know if anyone is interested in using this - there is some cost and work for me in setting this up and I don't want to do this unless it is going to be used.