It's not MMA, Matt!

lol
My first advice is to focus on the Kendo, and then wrap the rest of your training around it in a way that doesn't interfere with your practice and recovery. That will simply take experimentation.
You're on the older side (I've got 10 years on you, though), so recovery may be a bit of an issue.
I've found that I cannot do strength training more than two days a week without interfering with my martial arts practice. In fact, right now I am on a schedule of strength training every 5th day. However, that includes two Kumdo (Korean) classes and two or three taekwondo/hapkido classes.
I also do, at most, two, and often just one -- and sometimes none -- cardio/interval work in that 5 day cycle. It depends on how I'm feeling or if I've been lighter on the martial arts practice. Generally, the martial arts training get me plenty of cardio work. However, the major issue with running/interval work is keeping my legs fresh.
Depending on how strong you are, getting stronger will probably help. As I get stronger, I get faster. My once-a-week secret weapon is sledgehammer swings on a big tire. After that the jukdo (shinai) seems light as a feather! lol
Particularly early on (the first year for sure) the best support for your art is probably practicing your art. But, along the way, think about what seem to be your weak points: do you get gassed? Are you quick/explosive enough? How's the sword control? Then add in a bit more interval work or strength work as needed.
Have fun with the art, get invested in it, and supplement as you have time for/as needed or as you are able (given time, recovery, and other such factors).
Good luck and have FUN!!