Ahhh glad Craig saw this, he'll sort you out with set-ups
Ive been going through my car today and remembered a couple of things that might or might not help - hey, its always useful to have a reference anyway
The metal layshaft gear i was talking about is the optional Metal Top Gear ( Layshaft gear - the gear on the other end of the shaft which also has the spur on ) 21 tooth HD Steel Replacement part number 2794.
I had a problem that this fixed... took some time to work it out though

Basically after 4-5 laps i would lose drive. Get back to the pits, play with the gearbox, cant see or feel anything wrong. Rebuild the diff, check tightness, replace slipper, re-adjust etc etc Same problem, 4-5 laps and drive would go. Back to the pits, mysteriously fixed itself
Then i eventually checked the layshaft gear ( which was brand new ) the resin had deteriorated so after 4-5 laps it would heat up and melt over the layshaft pin losing its grip on the pin, spinning the gear around the shaft losing drive. Once left to cool down ( walking to the pits, swearing ) it would harden around the pin again just enough so it seemed it had fixed itself at the pit table.... And this was with an old 15 brushed double on 2400 ni-cads - imagine what brushless & lipo will do to a bad resin top gear
So luckily i found a old-stock optional TRX1 metal gear which went in one, and i used a modified TRX3 metal one in the other runner. It is just slightly wider though, binding the TRX1 gearbox. You can either play around with shims & ballraces ( not perfect ) or turn the gear down on a lathe about 0.75mm, which is what i did and is the better bet.
I never found the 30 tooth idler gear in plastic to be a problem, so i wouldnt worry about that one though. And the diff was and is a good 'un, great bit of kit that, tough as old boots
Again the resin gearbox U/J joints fail around the grubscrews, even new white ones fail quickly. Black resin ones are much better though, so if they are black use them. But another reason for the metal U/J gearbox joints though is it takes just a little bit of backlash out of the sliders, stopping just a little bit of 'wind-up' in them as you accelerate and decelerate. If you can find some, complete TCP metal U/J's are the best. Rare as though.
The main problem which affected both myself and Craig last year though was the resin parts deterioration. In the last race we both ran our TRX1's at we broke just about every suspension part there is in very minor knocks - we were both swapping spares just to keep them running...

Problem is the old white Traxxas resin doesent seem to have aged well - the later black parts are still fine though.
I hate to say it, but dont be suprised if even those new white parts of yours break at minor knocks, especially if its cold. The Traxxas TRX1 & 3 were known years ago for being the toughest cars on the track - now sadly that isnt the case

It depends how they have been stored and used. If they have been in the sun a lot they probably wont be much good. If they have been in a box somewhere sealed up they might be fine still.
The other things we used were the optional front 25 degree castor blocks instead of the 30 degrees to get some steering, and on my original TRX1 in the early 90's i modified the chassis to shorten the rear wheelbase on tighter tracks. Traxxas themselves also released a optional short wheelbase TRX1 chassis, i cant remember if it was any good or not though for the top drivers. I think Craig might have run one, i'm sure he'll tell you if he did.
Wheels are Ballistic Buggy Losi rears, with the outer middle machined to allow the nut to fit inside the rim, and slightly bored out if i remember rightly. And i used Ballistic Buggy Tamiya fronts as a perfect straight-on fit.
For the front brace i machined a couple of mm away from both the front arms to allow a brace to be fitted in 1.5mm carbon on the hinge pins. Together with a beefier bulkhead brace this worked a treat for the front end
Suspension towers i used Graphite Design ones in 4mm Carbon fibre, much better than the cardboard ones of standard ! If you need any, Fibre Lyte still do the shock towers for the TRX1 & 3.
I used the original 6- pin slipper then and now, as frankly im not a very good driver and just steering causes me trouble

Lots of other people used the Losi slipper or Hydradrive as you could get optional layshafts for them. Craig i know was hunting for one last year as he used to use one back in the day i think ?
If you can get it reliable resin parts wise, and with some minor mods it wont let you down and you just might be suprised at how capable it still is, especially on rough tracks.
Good luck - and try to post up some pics of it ?