Hi,
I know the TR6 gearbox is pretty similar to the TR4, which I'm familiar with, and would assume it's also difficult to get the retaining ring off the mainshaft to remove the gears, and equally challenging to reinstall? Seems to me I saw either Roadster Factory or Moss sells special tools for the job, but pricey at nearly $200 for the set, but nearly mandatory to rebuild the tranny. Another challenging thing is removing the large castellated nut at the rear, which is torqued to 90 ft lbs. There was a special factory tool with a long handle and pegs that fit into the 4 bolt holes on the flange, that attaches to the drive shaft, to hold the shaft from turning while loosening or tightening the large nut. It should be possible to make a tool, with a little ingenuity.
I agree that while the gearbox is apart you should definitely replace all seals, major bearings and the synchros, at a minimum. Some of the vendors sell all the commonly replaced items in a kit for a discount.
And yes, use GL-4 gear oil, again assuming the gearbox is essentially the same as the TR4. There are brass parts inside that will corrode if the newer GL-5 gear oil is used. I think it's sulfur content in the newer stuff that is the problem. It's not easy finding non-GL-5 in the local auto parts places here locally. But, I did see Redline synthetic at one shop, and that states it safe for this sort of gearbox.
I've not installed the J-type, have an A-type in my TR4 project car (not yet back on the road) and there are a number of other small items you'll need, assuming it's pretty much the same. There is a wiring harness and, probably, a couple switches that need to be installed in the top cover of the gearbox. To do this, the top cover must be drilled and tapped in the right places. A good shop manual provides all the details on where to drill. The switches operate by preventing the OD from engaging in certain gears, allowing it to engage in others.
The info about the actuating solenoid is correct, too. Proper adjustment is very important. The solenoid actually has two coils: one strong and one weak. The strong one pulls the lever to engage the overdrive, and the weak one holds it engaged until power is released. If not properly adjusted, the strong coil stays engaged and will burn out the solenoid very quickly. It's a little different arrangement on the J-type, than on the A-type I'm using. Your solenoid is horizontal, where it sits vertically on the A-type.
One other item you'll likely need is an adapter plate on the back of the gearbox, before it's possible to attach the OD. I know it's sold separately and required for the A-type. This installs first and there are instructions on safety wiring the bolts in the service manual.
Then when installing the OD you have to do a series of things, sometimes seems you don't have enought hands. There is an oil pump that builds pressure to actuate the OD, and the plunger for that needs to be retracted a little to allow it to slide into place on an eccentric lobe. At the same time, you'll likely need to have the gearbox in top gear, turning it to get the shaft to line up and engage with the OD.
It's a bit of a project, but certainly one that someone with modest mechanical skills can do. As others recommended and I've already mentioned a couple times, the service manual is very helpful. The procedure and all necessary accessory items are carefully spelled out, because ODs were fairly commonly added to cars by the dealers and their service departments needed to know how to handle it. I have Haynes and a good reprint of the factory manual. Each is useful in its own right and I often find myself double checking info from one to the other.
Good luck with your project!