Kealbo54,
I'm sure if people got to know you, see you ride to make sure you aren't mean to horses or the horses unsuitable to you, that you can ride and of course you'll need to waive liability, as horses are 'animals' with a mind of their own--so the hazard of mounting a stranger has to be lessened.
That said, I would get a hold of Cleburne's Division (reenactors group) which is in charge of registration, to see if there is a solution to things. Re-enactment safe horses is a horse that has years of exposure so, they are gold nuggets to those officers and Cavalry impressions who must get their needs met first.
At the 150 Chancellorsville, one guy would get off and another on to go into another scenario. So, do see what you can negotiate and always be open for suggestions.
Just some thoughts.
M. E. Wolf