Greg E.'s comments sum up the flaws with your version of the mechanism. While yours contains the same steps, it combines the nucleophilic attach and the proton transfer in a single step. Unless you have experimental evidence for a bimolecular step, the unimolecular step is much more likely. In this case, the unimolecular step is a 5-endo-dig cyclization, which is particularly fast. The alkene nucleophile is already present when the carbocation forms. The rate of the deprotonation is diffusion controlled, as we have to wait for a water molecule to find it.
Also, your logic relating the minority of the product to the unlikeliness of the mechanism is inherently flawed. A minor product does not occur at a lower proportion because the mechanism contains less valid steps. Instead, the distribution of products is related to the relative rates of different mechanisms and the relative energies of the products. That product is a minor product because some other product either forms faster or is more stable or both.
If this was on my exam, and I like the problem so I might use something like it, I would dock you a few points for combining steps that are not likely concerted into a concerted step. For example, if I decided this mechanism is worth 10 points, then you might receive 7 or 8.
Final note: Remember that experimental evidence trumps all else in science.
Regardless of how intuitively and aesthetically unusual your mechanism appears, if experiments support it, then it becomes a more valid mechanism. As an example of some of the non-intuitive things that are in "accepted" mechanisms, check out halonium ions and sigmatropic rearrangements, especially the one in the Baeyer-Villager Oxidation. Evidence in support of your mechanism might include a failure to observe or trap that final carbocation, a demonstration that the rate depends on the amount of water (since final deprotonation steps tend to be very fast), and others.