Lots of great suggestions here. Someone mentioned using the seat for power and support; something I might forget to mention without watching a person ride. If you’re not doing that already, expect it to take a while to make sense. But once you see the power you can get (and a little extra riding comfort when pushing down), you’ll wonder how you handled the rough terrain without it.
What’s your wheel and tire size? A fat tire is at its most useful under these conditions, so if yours is not very wide, consider an upgrade (if it will fit your frame).
Then your next best friend will be practice. Find the hard stuff, and work it over and over until you can master it. This applies with any riding technique(s), any wheel, etc. Nothing replaces actual experience. Look for new and different obstacles, trails or areas. Mix it up. Remember, the challenge of MUni is more about getting over the terrain than it is about going fast. If you were only interested in speed, you’d have more wheels.
You also mentioned you have a specific goal ahead, which is to be able to do well in a race. The requirements for racing will be different than for “regular” or “hobby” MUni. Speed is #1, and you don’t have to ride over anything that would make you slower than walking/running. So practice some of that as well, making dismounts before you hit stuff that will fall off, getting over it quickly, and not swinging your uni around where it might hit a nearby bike. Be courteous, and the bike riders will be friendly.
So let’s assume you want to be able to ride as much as possible over the next 5 weeks to cut down on running; a very worthy goal. This will rule out the hardest stuff in any case. Though you may be able to get through it, if it’s slower than walking speed there’s no reason to do so in a race (unless there are other unicycles, I guess). Anyway, concentrate on increasing your skills over the rough stuff, and at the same time, work on increasing your speed over those rough areas bit by bit.
Get some good wrist guards. Racing + learning to roll the rough stuff can lead to some good crashes, where hands always seem to lead the way! Leg armor is also recommended. For MUni and racing, knee coverage is probably more necessary than shin coverage, though the backs of your legs are also common victims in MUni dismounts.
Specific techniques for bump-riding are hard to explain in text, mostly in matching them up with the type of bump or terrain they go with. For the big hits, you have to lean back as described. For long areas of roughness you have to try and keep the momentum up. For dips, if you unweight the unicycle at the right time (like an almost-jump), you can sort of float over them.
Then there’s the terrain that requires picking your way through. For situations where you proceed one half-revolution at a time, the speed is so slow it won’t be compatible with racing so you might save that stuff for after the big event.
For best results, if you can get together with some other MUni riders in your area, they can show you more in a couple of minutes than you’re ever going to get from reading all of this…