I created Third Battle Invitational and was the meet director for the past 11 years (stepped away this year!). I also live a mile away and have run who knows how many thousands of miles there.
My opinion- Don’t wear a plastic plated spike if you have a rubber one available. The gravel isn’t bad right now (mostly mashed down into the dirt or worn away)and hasn’t been replaced in many years, but there are still occasional loose rocks that’s wouldn’t feel great in a shoe with a plastic plate.
A rubber-soled XC shoe is ideal there. The rubber plated Dragonfly XC would be fantastic.
About 1100m of the course is grass; the rest is crushed gravel or dirt, so aggressive spikes aren’t as critical as a full grass course. My teams and I have run fast workouts back there in just flats.
If you do go with the plastic plate, you’ll be fine. You’ll just have an uncomfortable step here and there. Luckily(or at least thinking optimistically) the rain will likely soften the trail a little, which would make them more comfortable.
Good luck this weekend!