I recommend a simple, inexpensive and very effective solution that will remove the rust and give you some low impact exercise.
Get yourself a pound of BBs or if that is illegal or requires too ma permits, get a larger weight of .177 ball bearings as well a a quart or liter mineral spirits.
Drain the tank, seal the petcock bungs , add the .177 spheres and about 1/4 of the mineral spirits, put on your favorite fast paced dance music and dance for about 15 minutes. The tank and content aren't too heavy so add a dance partner if you like.
When time is up, drain the tank through a strainer, to catch the .177s and have a catch container for the mineral spirits. keep up this routine until the mineral spirits exits clear. In your case I doubt you'll be dancing for any length of time.
USE fuel filters ! 70 micron inline filters are readily available. I tried to find the micron rating for the petcock and bango screens, but had no luck. The inline filters that are "E" proof for your turf are easy to replace, easy to check for softness. For those of you that are still riding on original ,OE prtcocks be advised that they use cork as a seal. There are kits available with modern "E" resistant rubber seals, Yada, yada.
I would keep the screens on the petcocks, if not junk, just to keep dead bugs, cigarette butts, and construction equipment stays out of the fuel line.. The screens in the banjos perform the functions of filtering and sealing the banjo. When they ave been subject to over torquing they neither seal or filter, they are not easy to remove, in situ) and the banjo bolt speeds the degradation process by cross threading. Yada, yada.
Your choice,
Best