Honestly, your axes might rust in those sheaths. I have the same chest from Costco doing the same exact thing. I keep a drawer for sheaths only. Side note: I love Costco! I got mine for $299, but it was our region’s regular price, and it was last year.
I removed the foam from my chest for reasons of rust. I use the shelving liner that GEC uses on all their “What’s Happening” section. I find this critical, because it allows the air to move underneath the knives. I have to keep the heat or air conditioning going at all times, to keep my humidity down, in my house. I also wipe all blades down in mineral oil, before storage.
It’s my understanding that INFI is really close to rust proof. I decided to test that. Warranty covers it. I’ve had a BAE2 out in the GA humidity, red clay, tree detritus, and rain for 5 days now. No rust or pitting has formed anywhere. I’m moving it every day to another area and simply wiping it down with my hand. The ground is squishing under foot her and has been, so the next few days, should be close to 90% humidity. It’s in a conifer now hoping to impale a squirrel.