Not making excuses for tour operators, but complaints are very time consuming. The ones that involve waiting for reports back from a third party can take forever. The third party doesn't have time limits to meet, and the tour operators sends ages chasing them for replies, just so they can try to meet theirs. You probably wouldn't believe the number that tour operators receive in a day! The genuine ones, and the not so genuine ones, all have to be dealt with in the same way. If people stopped complaining that they got served spicy food in India, that there was fish in the sea that frightened their kids, that the sand was too hot etc etc. genuine complaints could and would be dealt with far quicker.
In cases of hotels having no reservation for you, in the majority of cases it's because they've overbooked, not the tour operator. They overbook regularly, like airlines, relying on cancellations and no shows. When they don't get them the bump people. Unfortunately, unlike airlines there is not such thing as VDB and IDB, and Tour operators and bedbank guests are the first to go, as they both pay peanuts to the hotel. The hotel's direct bookers pay a fortune in comparison and don't get bumped!
As the transfer rep still had you on the manifest as staying at that hotel, the chances are the tour operator hadn't even been told. The transfer manifest is produced from the hotel booking manifest so if they hadn't booked you into the correct hotel, the transfers would be wrong.
Write to them telling them that you intend taking court action. Serve the papers and wait and see. We did this with Thomsons a few years ago. The court actually mediates via the telephone, to try to stop it from getting in to court (or they did in our case). It's obviously better from the courts point of view if it never gets that far. We sorted it out that way. It took 9 months in total. I didn't go near a travel solicitor, and wouldn't, free or not.