We have shared most of our race-training with monos. When we started sailing (cats) the club was dying, so another boat in the wednesday night races was welcome even if it was a raft made up of two pontoons.

Having a separate start is a good way to avoid the worst problems. Monos approach the line from further away than cats do and will luff you into irons the last few meters unless you have made a hole to dive into.
On the course, the ugly situations come while going downwind. Monos generally go a lot deeper, and are poor at keeping watch to their leeward. This is generally where a cat under spi or going wild downwind will come zipping in. You can never assume they have seen you, and even if you shout at them they need some time to jibe or slow down. Going up is not an option for them (they can, but are bloody stiff necked about it, and they need time to avoid breaking stuff if you take them too high).
I dont agree with Wouter that they often have rights over you. With the different angles cats and monos sails downwind, it's my experience that the cat most often will have established an overlap a long way out and will have luffing rights when the boats get close (assuming the cats are overtaking the monos of course. Please correct me if my interpretation of the rules are wrong). The funniest part is when some old-timer go hailing "mast abeam". Then we know it's time to jibe away..

Upwind there are seldom conflicts, just take care to not get in a position where you are a good luffing target (the stupid ones sometimes try to luff you, and loose time that way). You will not be around long enough to use tactical measures like backwinding on them. Just get by them no matter how, and if you go close to leeward, ride the lift in front of their bow if you dare to.

Keeping away from them during rundings is a good idea. Those boats are not very manouverable, and sometimes the crew loose control on them. "It doesn't matter where you go, as long as you go there fast" is a good rule, if it's crowded in the roundings (or look for the pinwheel effect and "slow down to win" as Rick likes to say). Remember that they will go high just after rounding the leeward mark, so be fast if they are to leeward of you.

When sharing the course with monohulls, we never assume they have seen us and never assume they will respect our right of way. This has proven to be wise time over time. I dont think they ever will learn how fast cats move in a decent wind.

Having a W/L course for the monos, and a triangle course with W/L for the cats is my preferred layout when sharing the course. Eventually, put the windward mark longer up.

I think Pete has it right. Find the real reason why they dont want to run races for you, and work on that. There is a lot of prejudices about multihulls, not to speak about beachcats among some monohullers. We are accepted in our small club now, after 6 years of attending all social, sailing events, volunteer work on the club house/area and holding office for the club. But they still dont understand why we prefer to zip around on a "childrens boat" like a Tornado instead of getting a proper boat. We just laugh at them and let them know that they dont understand what they are missing out on.