Radiant thermal film inside the covers?

Sounds legit to me, don't see why there isn't radiant heat from the bed especially (big hot area).

This calculator is handily set up for natural convection around a horizontal rectangular plate, and estimates both radiation and convective loss from the plate.

Results for a 100C 20x20cm bed in 20C ambient are:
* Convection: 27W
* Radiation: 25W
* Total: 52W

So about half the loss from the bed is convection, and half conduction. Total power required to keep this equilibrium is 52W. To confirm this total, compare it to the electrical power going into the bed (which with a bit of nouse can be measured). I would guess real values will be a fair bit higher, as this doesn't take into account the underside of the bed for a start.

This is all assuming no enclosure.

If the radiation is absorbed by your enclosure (acrylic will absorb far-IR) then part will be convected back into the interior air, and part conducted through and lost outside. The better the insulation of the enclosure, the more will stay inside.

If it's reflected instead, then it will go back into whatever can absorb it - which I guess would be mostly the workpiece and bed, but also the other non-reflective parts inside the enclosure. Then these would have to be a bit hotter relative to the above. You'll eliminate the proportion of radiation that made it out through the enclosure walls, which if the walls are thin will be significant, but if you have insulation already (even a few mm of acrylic does something) then it might be only a small amount.

So if you're considering keeping heat within the enclosure, then good insulation is the important part. Making the lining reflective with aluminium foil or a similar method would really just adjust the distribution of heat inside the enclosure - perhaps more in the part and bed, which may (or may not) be good for printing. For poor insulation, adding the reflective layer would reduce loss a bit. This would all be a bit tricky to verify.