Homemade sound panels

What kind of panels are you talking about? I've made some membrane panels and my only regret is that I didn't make them bigger. 6X3 instead of 4X2 would have doubled the material cost but that's insignificant to the labour and result. Membrane panels are more specific solutions for a narrower band problem.

Silicone around the edges of the pegboard or it might vibrate or, better yet, avoid it. The pegboard is the same as the wall that you're trying to get away from. If the pegboard were in front and not touching anything, that would be a membrane but not a good one.

The foam might be better aesthetically but it's less functional than double thick 705. For a single layer of 705, I would expect reduced effectiveness below 200 Hz. Double thick is fairly effective, with the air space behind, down to 100Hz.

Pegboard will only act as a resonator if it is free to resonate and not touching anything, except at the edges. The holes mean that it cannot be sealed and damped, which is not critical but helpful. The idea being that movement is disssipated into heat.

Cotton is preferred to synthetic.