Wow, sorry about the nail in the side.
The contractor must be referring to the outdoor txv since he has to remove all the refrigerant. Otherwise if it was an indoor txv change out they could save the gas as the compressor can pump all the refrigerant into the outdoor coil and can be sealed in there temporarily. (called pumping it down)
Now you mentioned the compressor not coming on at all? That is not typical of a TXV problem, at least not initially. A side symptom is the high pressure switch will come on (open) to cut off the compressor, if that txv is clogged up, but I am surprised the compressor will not operate at all. Even after the unit has sat for awhile (pressures stabilized) it should come on albeit for a short period possibly.
Threre are a lot of questions you could ask your contractor to get more info.
1.
Find out which TXV is bad (indoor or outdoor) and how they diagnosed that with a cut out compressor.
2. there are other possiblilites. Maybe they overcharged it with refrigerant and it is cutting out on high pressure.
3. Ask what the superheat/subcooling is and learn yourself so you know you are not getting a line.
If you can get a little more info it would go a long way to finding some real answers for you.
Here is a vid on TXVs and it is acutally on a lennox indoor coil and a pic of a lennox outdoor txv.
video on you tube
photos of an outdoor txv on a lennox unit (halfway down I think)
Judging by your intermittent problem in heating it sounds like that outdoor txv was getting clogged up and your unit cutting out on high pressure in heat mode.
To directly answer your question yes there is history on the outdoor TXV being a problem (if that is the one they diagnosed)
And yes when they opened it up maybe they did a less than stellar job pulling a vacuum, not changing the filter drier, not brazing with nitrogen flow etc that contributed to it clogging up for good.
You also said it does not run at all in cooling mode either? Even after sitting for a couple of hours idle?