I wish I could give you answers because you are using exacly similar settings as mine i.e. a heating mate under a large container but I am new to rootings of cuttings. I started mine two weeks+ ago with heating mate. The only difference is that your cuttings are rooting well and mine are leafing well but with miniscule roots and just iniials. I am using the baggie method and have transferred some cuttings to Perlite-Vermilite mixtute. The cuttingss have leaves and I hope (& smetimes pray) that the cuttings will root eventually. I am not rushing them but wish them to survive and root sometimes until spring.
That is why I will be interested in expert answers to your post.

I'm by no means an expert, but I do know that:

You should let the soil temperature be your guide. If it's lower than 72-75* F., the optimum temperature for cuttings to root, (especially if air temps are a little cooler than soil temps) a propagation mat would be helpful.

... and that soils should contain good amounts of moisture w/o being soggy, and they MUST contain good amounts of air (the more the better). Let this be your cue as to whether or not you should irrigate the soil.

Tenting cuttings to keep humidity up until roots form is always a good practice. I never fully enclose cuttings, however - not even when rooting in a bag. I keep some kind of opening in the tenting or snip a corner off the bag so there is some air flow to prevent fungal issues.

Al

Last year my rooting setup was a heating mat under the lid of a large plastic box, with the box inverted over the lid - like a mini greenhouse. I was able to gradually increase the air circulation by lifting an edge of the box onto different sized supports. This helps greatly for weaning the cuttings off high humidity.
With larger rooted cuttings two boxes of similar width and length were used, with the shorter box on the bottom and the taller on top. It was a little precarious, but it worked.
I put the unrooted cuttings still in bags on top of the "mini greenhouse". The mat was set just below 80 degrees during the day and just above 70 at night. One problem I noticed was that the paper towels wrapping the unrooted cuttings in the closed bags dried out on the bottom. That surprised me; I thought the humidity in a closed area would keep them evenly moist. It was an easy fix, I just turned them over in the morning and at night.
I did some horizontal cuttings in sand and the sand also dried out at the bottom while the top still looked moist. I didn't seem to have that problem with the cuttings I had potted in pearlite and soiless mix in cut-off water bottles.
This setup was a variation of one mentioned last year on FF. I thought it worked well, and would appreciate hearing how you make out.

For the past 2 years I've done my cuttings in a larger storage container with a metal basket (turned upside down) in the base. On this base I put a seedling mat and then above that a seedling tray (with holes for drainage). Into this I put 16 oz cups filled with Perlite/Vermiculite and the cuttings. I start with the cover mostly on (but never sealed) and as time goes on I move the cover more and more open (til it is sideways and only covering the middle).

Most things root well, some stubbornly refuse, though I haven't had problems with rotting as badly as I did before using the seedling mat.

The room I do my rooting in is not cold, but is not as warm as the remainder of the house (though I may change locations this year). I'm sure the warmth provided by the mat and the humidity from the water that collects below help the overall process.

~Chills