Currently, "that" has three values:
Result: pro:rel|that^pro:dem|that^det:dem|that
You don't mention the third, which is involved in sentences like "that man is my father"
You are basically asking to add a fourth reading of conj|that. You are suggesting that we add the reading conj:sub|that. In fact, we changed all cases of conj:sub to just conj over a year ago. So, it would be conj|that. Perhaps you have an old version of MOR. But this is just a cosmetic renaming in any case. I agree that it makes good linguistic sense to add conj|that. If successfully tagged, that form would apply to lines 29 and 89 in your example transcript. However, for this to have any impact on what you are doing, we would first have to go through the training corpus to see if this usage is even present with any frequency. If not, adding it will have no effect on POST. And then there is the question about whether it is present in sufficient quantity to result in good tagging. This will take time and it is hard at this point to say whether it would work out reliably.
Going through your example file, it is clear that there are errors in disambiguating "that" beyond just the problem with conj|that. There are also two cases in which something should be tagged as pro:dem, but is tagged instead as pro:rel (lines 69 annd 95). I see in your corrected version that you properly recoded these as pro:dem|that. In both of these cases, it appears that the demonstrative occurs before the word "is". I could add the following rule to POSTMORTEM that would cover these cases:
pro:rel|that cop|* => pro:dem|that cop|*
However, to avoid overgeneration, this should really include a "not" as in
^n|* pro:rel|that cop|* => ^n|* pro:dem|that cop|*
That would probably fix the majority of these problems. However, this will require a modification to POSTMORTEM. The good news is that we need to make this modification anyway.
However, there is no way to use this POSTMORTEM method for adding conj|that. For this, the best approach is a version of what you are doing. You search for pro:rel|that and revise to conj|that. This should only take a few minutes for each file. You could also go a bit faster perhaps if you search for pro:rel|that with KWAL and then use the output to triple click and go to cases where you think a change should be made.
I'll address your other question separately.
Best,
--Brian MacWhinney