In 2012 there was free dumping of used sanitary water at the parking lot of the soon-to-be-built museum - across from Mike Crawford's CarQuest shop. I don't remember if there was a water spigot there - but maybe by now there is. Otherwise - that tap at the Pilot truck stop is available. Mind that you have a hose with you to get the water into your tank.
You're welcome, I assume, to park your RV in the Museum parking lot. No utilities (other than the afore-mentioned sewer and maybe water), but it's free and the closest you can get to the salt and still be in town (so to speak).
Where will you be renting your RV? We got one from Salt Lake City bank in '01, and the place did not ask if we were going to the salt flats. A rental place in SLC might, by now, be wise and ask for a destination. If you rent from someplace farther away -- Las Vegas, or Los Angeles or San Francisco - - they'll never think to ask where the heck you're going. Whatever -- don't tell them that you're headed to Bville or they'll probably get snippy and force you to either abandon your idea of renting -- or have you sign a waiver and still have to pay hundreds of dollars for cleaning. Beware.
As for electricity -- do what you can to afford to rent an EV with built-in generator. It'll (of course) give you freedom from needing a hookup. Sometimes the generator doesn't add anything to the basic rental price - but they'll get you on the hourly charges for using it.
If you haven't tried the KoA - go ahead and give them a call. JB says they're full -- but maybe there's a waiting list. They've got full provisions there -- even wi-fi, I think. Their phone number is in the Rulebook (near the end of the book).
Finally - the Bend in the Road has unlimited free parking for RVs. It isn't necessarily the quietest place thanks to late night revelry, but there's always someone that you can chum wit. If you want less noise -- you're welcome to drive up the hill a few hundred yards from the Bend - - and you'll find lots of space and silence.