Oh man, now you've gone and done it Ken! The four gears are great fun, but be advised the hoighty toightys will correct any poor nomenclature. It was the last slot car I purchased in my youth. I think it's best to put the following blurb here. We can move/change it later
The Specialty chassis had a full width dragster tire, or low pro tire depending on the model. I've used the replacement silicones for years. Jag Hobbies has them. Slotcar Central used to carry the original stock silifoams, which I have not used. If the original silifoams arent too awfully baked, (read still slightly pliable and not crusty) you can reconstitute them using 99% isopropal alcohol and flowable clear silicone. Pump some alky into the tire by massaging with your finger. It should push back if it's a viable candidate. I like to pump them clean of any large amounts of debris, specifically foam duff.
Then massage some alky thinned silicone into the foam. Put the tire on a mandrel. Smear the contact patch evenly, spin the excess off, and stand them up to dry. After they dry, I'll scuff them around with some 220/320 paper on my truing pad. The above being somewhat similar to the approved technique for making your own silifoam tires.
The dragsters featured a 5 ohm blue/gold armature. Although coveted at the time, many have poorly centered comm plates, making them little more than a novelty hand buzzer. Also notorious for slinging their winds, a light brushing of thin epoxy, will keep them from suiciding. Many have been pilfered from the original dragsters. Still and all, a good blue drag arm is great drop in fun. The Specialty chassis also used a 12 tooth pinion, rather than the standard 14 for AFX. Keep in mind that because of the added gear, the magnet positions are reverse polarity from the 3 gear chassis. The rear axle is unique due to the tubbing of rear chassis.
Every half width rim, has a full width rim hiding inside. A good arbor is required. Otherwise a sharp blade is all it takes. Keep the speed down and let it cut. The half width rim provided lateral clearance on the rails for road going models that the dragsters didnt need. I personally use full width rim for either profile, for the most part, with no issue. Typically, I'll cut the full width lopro, if I actually need the 1/2 size.
Notably, wider is not always better. The relationship is not linear. At some point, power and traction zero out, so that any excess becomes un-needed drive train weight. A tidbit I got from Sriggs, of Yellow Jacket fame, and later discussed/supported in a Harden Creek wheel and tire expose.
Overall, I have a Specialty check list that developed over the years.
You'll likely see some heavier cleaving on the toe of the pick up shoes. More so on the dragster. As the shoe and hanger geometry is identical to a chassis with .474 rear tire, the arse up stance tips contact patches require attention right from the get go; for them to ski properly and provide a reasonable service life.
Take a moment and sight in where the armature gear meshes with the big idler. The big idler has a halo. If the armature gear is not pressed correctly (too high); the comm thrust forces the armature gear up into the halo, potentially canting the big idler on it's post. Also mandatory in my Specialty world, is gear lapping, both frontwards and backwards. The rouge need not be overly aggressive, medium automotive polishing compound is a good starting point. Finish with a gritty toothpaste. Water washable and minty fresh.
Check for excessive clearance between those jumbo rear wheels, and the chassis frame. Typically they dont get pressed all the way back on if someone has had them apart. Also be on the look out for the wobble
I never met a Specialty chassis that didnt benefit from one or all of the above.
For the casual hobbyist, and where roolz arent relevant, the best low buck modification is changing to an AFX 6 ohm armature in combination with the above checklist. Road racing snarling Specialties is good fun!
Good luck

,
Bill
Where some must die, so that others may live.