OrlandoEnglishTutor“CJ, you say it's correct only in the negative, but I would say it's common usage in the positive also:
I practiced and practiced that piece until at least last I could play it without errors. (You say that is incorrect and must be "i was able to"?)
My son tried to lift the weight in spite of my telling him it was too heavy, and it turned out that he could lift it! (Incorrect? Must be "he was able to lift it"?)”
This isn't really the subject of this thread, but in any case ...
First of all, when I say it's correct only in the negative, I'm only recounting observations made in reputable sources like Palmer (The English Verb) -- though I do agree with their main point. Secondly, we are only talking about the reading of could in which we succeed at an attempted action -- not the case in which could expresses some general or habitual ability in the past.
The example which acts as the "poster-child" of this phenomenon is as follows.
*We ran to catch the bus, and we could catch it.
This is consistently listed as ungrammatical when taken in the reading: ... and we did (succeed in catching the bus).
(And anyway, I don't know anybody who speaks like this, using could to mean 'succeeded in an attempt'.)
Nevertheless, the same sources consistently point out that the following is grammatical.
We ran to catch the bus, but we couldn't catch it.
(meaning we failed to catch the bus)
The examples I've seen which attempt to illustrate this point have all been in independent clauses. I don't know whether that is significant.
Your examples seem to show that perhaps in the right context the phenomenon is neutralized, as in an until clause or a that clause.
In the case of practicing, however, I don't see the ability to play a piece as a one-time successful act. Rather, practicing is the acquisition of the skill needed to play the piece at any time one wishes to play it, so could is fine. This is a different reading of could than attempting a 'success' reading of these:
*I could [play the piece / lift the weight / ...] the first time I tried to.
*[The first time / As soon as / Once / When / ...] I tried to ..., I could.
I find this turn of phrase defective, though I must admit, not always fatally so. 
The weight lifting example is more difficult to explain. It turned out that or ... found that might so strongly suggest the success-at-a-point-in-time scenario that could can pass through without notice. I don't know. I wonder what Palmer and his buddies would say.
CJ