You probably climb harder than me, so take this with a grain of salt. There’s a lot to say on the topic of mixing endurance training with climbing training but I’ll start it off with the recommendation to start a hangboard regimen. Hangboarding in general is one of the best tools to improve climbing ability (besides climbing), and is particularly effective when you’re trying to balance climbing training with endurance training because the recovery time from hangboard will only minimally interfere your running training and recovery. Ie–you should find it possible to overlap running and hangboard without too much added fatigue.
ARCing (high-volume continuous easy climbing for endurance) and power work (bouldering, campus) are important climbing training tools as well, but the problem is that these are much more demanding overall so it’s easy to venture into overtraining land when mixing them with running training.
If you don’t need to peak both running and climbing fitness simultaneously, your best bet will be to alternate periods of focusing more on climbing with focusing more on running. Whether you have time to achieve a peak in climbing fitness this year before your race will depend on your training history in both sports.