Hi anchorman,
The best source of guidance about whether your support system would be suitable for your mattress would be Imperial Bedding. I would also keep in mind that if you are using a rigid support system of any kind instead of their box spring then it will change the feel and performance of the mattress and will have an effect on its durability as well.
In very general terms … I would suggest that if you are using a firm non flexing support system instead of a box spring that the gaps between any slats in a support system are less than the diameter of the springs in a mattress (say 2" - 3" depending on the springs) so that all the springs are more evenly supported. If the gaps between the slats are just a little wider than the springs then using something like the pegboard attached securely to the slats and the side ledges would be a suitable way to improve the support but you would still be compromising the feel and performance and the durability of the mattress to some degree compared to using an innerspring that is designed to be part of the 'sleeping system" as the support system under the mattress.
A piece of plywood would be strong enough to prevent any sagging but would also be an additional risk factor in terms of providing ventilation under the mattress and the possibility of developing mold or mildew under the mattress (see post #10 here). I would also keep in mind that while the T-slats themselves wouldn’t sag … softer comfort layers on top of the mattress could still be sagging into any gaps between the slats and if a material such as pegboard or cardboard ends up sagging into the gaps over time then the mattress will just follow any sagging in the support system underneath it.
If you are looking for a thin, strong, and non flexing support system then a suitable slatted bunkie board (usually about 2" thick") or something like the slat conversion kit here would make a strong, thin, suitable, and relatively inexpensive choice with good airflow that would have no risk of sagging even though they still wouldn’t be ideal compared to a box spring in terms of the overall feel and durability of a mattress that is designed to be used on a box spring that has some flex underneath it. Something like the Ikea bed bases here may also be worth considering and would provide some flex under the mattress.
I should also mention that I talked with the owner of Imperial Bedding today just to make sure that my comments are “accurate” and based on decades of experience in manufacturing mattresses he would agree with the comments that I’ve made here as well.
Phoenix