I never ran regular cycle tires on my bike, at least at any significant speed.
They were car tires, specifically Goodyear Frontrunners, Rear was a 15" tire (intended for the front of a SuperStock car) and front was a 17" (intended for the front of a Top Fuel dragster).
I don't remember what pressures I was running, nothing very far off of what one would use for a typical moto tire, in any case.
The guys who were traction-limited tended to run roadrace rain tires on the rear.
Those were the guys who were running in the neighborhood of 200+mph with miserable aerodynamics.
They seemed to work fairly well, but wore out pretty quick....
El Mirage is a fairly short run (1.3 miles), so there's not a lot of concern about heat build-up in the center of the tread.
Bonneville is a 3 or 5 mile run, depending on whether you're short course or long course.
At that time you had to run >175mph on the short course to be allowed to run the long course.
Even at ~200mph, the short course was long enough to get up to speed.
I'd run out of Nitrous on the long course....
Heat build-up in the center of the tread was a problem for the 200+mph with miserable aerodynamics bikes.
I saw a roadrace slick with an inch wide strip chunked out all the way around from excessive wheelspin.
For the application in question:
I'd run the front at a cold pressure equal to what you would want to see as a hot pressure on a roadrace track.
For El Mirage or Bonneville, you're not going to get any appreciable heat into the front tire.
For the rear, I'd run a cold pressure 3 psi or so below what you would want to see as a hot pressure on a roadrace track.
Then I'd check it right after the run.
I've not run there in over 10 years, and never with regular moto tires, so... not really all that helpful.
The existing El Mirage 650cc gasoline record:
(A-G)
no fairing 168.488mph.
(APS-G) with a fairing 174.249mph.
Those records are from the time period when I was there, that guy ran for *many* years to get 'em.
The existing Bonneville 650cc gasoline records:
Modified Gas
no fairing (M-G) 157.556mph
Modified Partially Streamlined Gas (MPS-G) 171.324mph(*)
(*) This record is 33 years old, and thus may seem to be ripe for the picking.
However, it was set by Don Vesco, an absolute ICON at Bonneville.
And, AFAIK, it was set with a sleeved-down TZ-750 2-stroke....
With more details on what you're trying to do, I can likely help more in general as far as running the bike and such....
Bonneville and El Mirage are very different in many ways, but do share the characteristic of being the most inhospitable places on earth to compete.
Many folks underestimate that part of it.
Both are usually brutally hot, and Bonneville often has high humidity as well.