Yes, Swinging Bridge is where Buckhorn Wash pops out and joins the San Rafael River. The road then keeps going south to I70 at the Sinbad interchange (not sure what exit that is?), but if you cross under the freeway there you will be on Temple Mountain Rd and headed for Reds.
The Muddy does run by the base of Tomsich, and the Reds Canyon Rd will take you there. If you spend some time out of the rig tromping around the mine areas at Tomsich and Lucky Strike you could spend a whole day in there easy. The problem with giving advice about touring the Swell is there's so much to see and it's hard to know what pace other travellers like to move at, but if you wrap up in Reds and have some time, consider driving over to Temple Mountain or down to Hidden Splendor, two more mining areas with great scenery.
AWESOME! Thank you for the information. Last night I was reviewing the tracks that we recorded when we were there in April for the first time and trying to map out a rough plan. Currently I have a plan in my head, but it's only written in Jell-O now, as it's not solid.