I feel my attempt at hints are actually just muddying the waters. Let me step back and try to be explicit in my question, while not giving away the answer.
The bicyclic ether is the correct product. You note in your first guess that there are several competing pathways which are possible. In your first guess, you went with THP formation first. In your recent guess, you go with THF formation first. Which do you think is more plausible and why?
Separately, what I was trying to say the first time is: the researchers did not initially attempt the one pot reaction. First attempts were 3 sequential steps with purification between. Thus, the product of the first acid step can be isolated, treated with base and a second intermediate can be isolated, then treated with acid again to isolate the desired product (which you've drawn). Based on your mechanisms (first and recent), if you stopped your reaction after the acid step, you would not isolate the product the researchers do, etc. While your transformation is correct, the elementary steps are not.
More clear, or more muddy?