I would get the steering rack looked at.
That violent ratchet action on the steering wheel can be caused by hydro fluid pressure.
Example: If someone installed the In/Out lines in reverse order, that's exactly what can happen. Violent, and very fast steering wheel ratcheting. Strong enough to break bones if caught in the wheel.
When Air is inside the system, this also causes a bad ratcheting to the steering wheel, but is less violent. It can feel like it is shaking the entire vehicle, and in fact it does.
I have no idea about a new boot. :scratch:
Side to side rotational play in the steering shaft is normal in older higher mile rigs. If yours has "Wollered" out...The cheap fix to this is to source a low mile version from a salvage yard. There is a plastic & a steel version. The steel is stronger and lasts longer. Only a 2nd gen for a 2nd gen will work. Up and down movement for the slip shaft is at least 3". There is a sticky thread covering this in the 2nd gen forum.
As far as the inner TRE, any play is a bad thing. This should be changed asap, as it will only get worse, and with it, comes steering issues. I can see the hammering of the rack doing harm to this part fairly easy. A re-manufactured rack comes with new inners on it usually.
Look for fluid leaks on the cross member and around it. Check the steering fluid levels, and for bubbles. With the engine running, turn the wheel left to right a few times. It should be quiet. Is it? or is it louder then normal? Turn off the engine, look inside the tank. Does it look low? Any tiny bubbles or foam on top? Check the lines to the pump & the rack. Remember that the line to the tank & rack is supposed to feel loose at the nuts. The others should be tight with no play. Just look for leaks.
Ok, if all that checks out, the only other thing we have not talked about in this thread is the steering pump itself. If it is bad, it could also play a factor in the shake. If it is partially clogged, it can pulse fluid pressure.
Normally, a bad shake in the front is caused by bad ball joints, bad TRE's, or a busted tire belt. You say they are all good, except the recent notice of a little play in one inner tre. So this is why I am thinking the rack & pinion.