After reading up on recipes and some related forum posts, I decided not to go through the trouble/expense of buying and mixing up actual Retr0brite paste, which contains glycerin and xanthan gum, and instead focused on the active ingredient: concentrated hydrogen peroxide. Recipes typically call for some low-concentration, aqueous hydrogen peroxide, like you find in the big brown bottles, bolstered with OxyClean--basically dehydrated hydrogen peroxide powder--and thickeners to make a paste that you can spread onto things. This in mind, it doesn't make much sense to use relatively expensive low-concentration hydrogen peroxide as a base when you could just start with regular water and add more OxyClean...
If you have access to a Sally Beauty Supply store, they sell bottles of 40 vol creme developer, which has an even higher concentration of hydrogen peroxide than OxyClean and is already goopy, so you don't need to fool with the glycerin/xanthan gum to get it to stick to stuff. This can be helpful if you don't have an appropriately sized container in which to submerge your plastic, and reports suggest that it works within hours rather than days. However, you need to be more cautious with this, as it can damage clothing and skin/hair.
Anyway, I skipped the low-concentration stuff and just dumped a bunch of OxyClean into a roasting pan full of water, plopped the top section of my SNES Mini in and left the whole thing out in the sun for 2 days (you'll have to replenish the OxyClean periodically, as it seems to lose its mojo over time).
The first day, I didn't put nearly enough OxyClean in, so there was very little improvement. The second day, I drastically increased the concentration and had much better results. I found that, in a properly high concentration, the plastic should be more buoyant than the solution, so you'll need to hold it down with something. Also, there seems to be some disagreement as to whether the process needs actual sunlight or if any light source will do. In my case, there was no effect from 8 hrs under a CFL light bulb, so the sunlight (or a UV lamp) seems to be necessary.