I think it's possible to bleach plastic with hydrogen peroxide, but this tidbit from a Wikipedia page is very relevant:
"Hydrogen peroxide is an inefficient bleach below 60 °C, but when activators such as TAED are present, hydrogen peroxide (in the form of the perhydroxyl anion in the alkaline water) can react with the bleach activator in a process called perhydrolysis to form a peroxy acid (also known as a peracid). Peroxy acids are more efficient at bleaching at lower temperatures like 40 °C."
Oxiclean contains both sodium percarbonate (which releases soda ash and small amounts of hydrogen peroxide) and TAED. Thus, I posit, the active ingredient in the actual Retrobrite recipe is peroxy acid of some sort. I also posit that Retrobrite reaction speed does correlate with temperature, especially if one is only using hydrogen peroxide.
I plan to perform a few tests.
1) Denture Tablets
Yes, you read it right. Denture tablets theoretically have everything necessary for a Retrobrite reaction.
"Citric acid, FD&C blue #1 AI. Lake, FD&C blue #2, flavour, polyethylene, glycol, potassium monopersulfate, sodium benzoate, sodium bicarbonate, sodium carbonate, sodium lauryl sulfoacetate, sodium percarbonate, tetraacetylethylenediamine, VP/VA copolymer."
The sodium percarbonate will release small amounts of hydrogen peroxide and the TAED will react with it to form peroxy acids.
2) Sodium Percarbonate
Do you need TAED to achieve functional Retrobrite? Can lower concentrations be used, such as the 3% that a fully dissolved solution of sodium percarbonate achieves? I'll find out. I may also try denture tablets with a sodium percarbonate solution -- their TAED could be useful.
3) Temperature
Does temperature change the speed of Retrobrite reactions?
4) UV Light
If peroxy acids are present AND the water is heated, will the bleaching process occur without UV light? If UV light is present without significant heat, will the process still be accelerated? I have an LED UVA light in the 360-370nm range on order which will help in determining whether UV has an impact -- wouldn't it be crazy if it didn't have any effect? Sunlight may just be donating heat energy through UV radiation and nothing more.

If anyone has a yellowed keycap set of any mounting type that they wish to donate for science, PM me.