I think that in addition to regulating your humidity, you absolutely must
regulate air movement (many people here, myself included take cheese out of the cave a few times a week to give it air, but it's not nearly as effective as a microorganism-full cave with a healthy dose of oxygen movement). The other thing you need is to
give your microorganisms a place to call home. The food-grade plastic walls of the freezer aren't good enough.
For air movement, use a small computer CPU cooling fan. you just need some air movement. No need to go crazy or have a 2nd pulling fan. Too much air movement will carry out the microorganisms and moisture that you want to keep in. If you use a computer fan, a small ventilation hole may be enough to let air out. You may find out that you don't even need to let air out but just to circulate it in.
Another option is to insert a hose from an aquarium air pump right into the cave. This is something I have been doing for the past 10 days so it's still an experiment and I don't have final results, but unless I have some weird B.Linen invection in my cave it seems to be an incredible success. The cheese is responding incredibly well to it and blooming like a garden in the spring... In spite of bringing fresh air from the outside in, theambient humidity in the cave jumped 10% up. That is because the air hose circulates the moist air and creates a convection rather than letting moisture collect as water beads. I shut the door on my hose and it bends the magnetic door rubber seal slightly around the hose, opening just enough space for excess air to come out.
To give your microorganism a home-sweet-home line up that freezer chest with wood planks or bricks/terracotta/baking stone. (or combine). Create a porous cheese cellar, even if it's very small. My cave (wine fridge) came with wood shelving and I partially cover the shelves with straw. I have plans to actually line the interior with tiles or bricks in the coming weeks.
If you haven't done so yet, get one of those cheap digital combo thermometer/hydrometer devices. You mentioned in another post that you are in South Africa so here's a local South African example for 89 Rand
http://www.bidorbuy.co.za/item/38774076/LCD_Digital_Temperature_Humidity_Meter_Hygrometer_Clock.html. You may be able to find it even cheaper. I have a bunch of these here. I use them in the warmest and coldest parts of the cave, and in the kitchen during cheesemaking and at the drying area when draining or drying cheese. Sometimes I also put them inside ripening boxes if needed. Get yourself a few.