Sorry to be so late to this party. I am gratified that folks are using my website. I learned a lot from experienced guys, as well as by doing. The website is my way to return the favor. I have unfortunately not been keeping my website up to date (my bad).
On the rear I still plan to use the Goodyear 2286 28x4.5-15 tire mounted on Centerline aluminum 15-inch wheels made for early Volkswagens. These wheels have about a 6.3-inch (160 mm) diameter center hole, which fits nicely over a sprocket carrier and also over my custom HCS front hub. The 2286 is (using polite language) difficult to get on the rim; there is a danger of damage to the rim or the tire. I ended up drilling out the rivets and replacing them with bolts. Problem solved, albeit with considerable work! I spread a thin layer silicone sealer over a large area between the wheel halves during assembly, instead of the large OEM silicone caulk “rope” that I think could fly out of the rim valley at speed.
On the front I am in the process of switching from Goodyear 2282 21x5-15 to the new Goodyear D2904 22x4-17 Frontrunner. It has a more rounded cross-section than M/T or Goodyear Land Speed tires, and also costs less. Admittedly the fastest guys have used such tires on 2-wheel liners, which were the best option at the time, but I still worry about weird handling due to jumping from one shoulder to the other of flat tread tires. As Rex mentions, Goodyear and SCTA have authorized the new D2904 Frontrunner for LSR use up to 300 mph, at 90 psi and less than 1200 lbs radial load. This tire requires a motorcycle wheel bead shape, which has a slightly smaller than a car wheel bead shape, as discussed in detail on another forum thread. Perhaps a car wheel could be modified. A custom wheel can easily be had - be sure to get the correct motorcycle bead. I bought a pair of older model Weld Racing dragster front wheels on eBay. These wheels have the appropriate bead shape, with spindle hubs and a solid disk center - no spokes. I milled out most of the center section (does anybody need a set of spindles?) and made an aluminum adapter disk to fit the Weld rim and my hub (I am stuck with the early VW 5x205 bolt pattern). In retrospect, a custom wheel would have been a better option, taking my time into account. I will look at the All American Wheel that Rex mentioned - I did not know about it.
Overachiever John Buddenbaum used link front suspension/steering on his IMHO brilliant BUDDFAB motorcycle streamliner.
BTW, the current SCTA S-F-1000 and the AMA S-AF-1000 records were set in 1967 by a guy (now deceased) by the name of B. Munro, as is loosely documented in the entertaining movie "World’s Fastest Indian" and more factually in a book entitled "One Good Run." There is a strong sentiment among many LSR people that this record should not be broken. Just saying.
I hope to see you on the salt - though probably not this year, unless it dries out soon.