Cystitis is constant loo trips producing small or no amount of urine, if Cassie pees normally just not in the tray its not cystitis as such, typical to give ABs before checking for infection
Read here for interesting info on FLUTD, a very small amount is actually caused by infection!
http://www.mpmproducts.co.uk/?in_section=health&page=flutdHopefully once the sample is looked at you will have a better idea what to change, it may be dietry or if nothing shows up then you need a behavioural approach.
Things i'd implement:
Extra tray or 2, some cats like a clean tray each time
Remove a hood some prefer open trays
Remove litter tray liners and that horrible deodouriser stuff if used
Place trays in different areas, quiet low traffic is best
Try a tray of fine litter, one like sand in grain size
Clean the offending areas with a proper enzyme based cleaner
Try her on Cystaid supplements
If its stress based then plug in feliway and try zylkene supplement and try to improve on the stress trigger