No. As I said before, and as the quote I provided states, the homeowner's rights depend on a breach of the contract. In contract law the term failure to perform means that a party has not done what the contract required him to do, and thus is a breach of the contract. So it is not ambiguous. The homeowner could not simply terminate the contract for just any reason. But when the contractor has breached the contract that would be one potential remedy for the homeowner. And the OP certainly is not dumping the contractor for some reason unrelated to performance of the contract. According to the OP the contractor has done a shoddy job of the work and after a month has failed to come back and remedy it despite a promise do so. If accurate that would be a material breach of the contract. So the homeowner's right to sue for breach of contract flows from that.
Two attorneys can argue over the case law if the case law is somehow not clear, there are conflicting cases, etc. Here, though, the problem is that no statute or case law that I can find in Texas says that there is a right to cure in this circumstance, and the two Texas lawyer articles I mentioned earlier back that up. Again, you wouldn't need to put a right to cure in contracts in Texas if the law already provided for it. Certainly the contractor's attorney could try to make the argument for it anyway, but given the lack of any law in Texas supporting it, that would appear to be a losing effort, though the lawyer would get paid for it whether he won or lost the point.
And in any event, the homeowner has already given the contractor a chance to come back and make it right — and the contractor failed to show up. And it's been now over a month since the contractor was last there. So even if there was a right to cure it seems to me that the homeowner has provided that opportunity. It doesn't seem as though this contractor is at all interested in trying to fix the problem and provide good service to his customer. What more would you think the homeowner has to do? Get down on his/her knees and plead for the contractor to fix it?As a contractor yourself I'm not surprised that you are in the contractor's corner on this one and expect the homeowner to bend over backwards to give the shoddy contractor all kinds of chances to fix it, but the law in Texas does not demand the homeowner do that.