I took a chance and ordered the 4XH0S69185 kit from Provantage. The model and the image are identical to what is listed on Lenovo's site as being compatible with the P53 and P73 (and P72 also).
The same kit is for sale on Amazon Marketplace for 3 times the price. However, since Amazon allows you to zoom in on the image, I was able to tell that the short HDD connector has the cable on the opposite side than what would be required for the P53 (if you compare the P53 and P72 manuals, it becomes clear that the cable seems the same, but is mirrored).
It seems to me that the compatibility for P53 is actually possible because of the long cable included in the kit. If you were to mount the HDD backwards (connectors facing the opposite direction than what is shown in the manual) then the long cable would go around the HDD and connect to the motherboard properly. The power, data and actual cable seem to be aligned properly in this scenario.
Since the kit went out of stock yesterday, I'll have to wait for Provantage to receive more before I get it and test it. I'll return with conclusions if no one else beats me to it.
As a side note, between the hard time I've had finding this part (which I'm not 100% convinced would work properly*, so I basically pay to test it) and the BIOS release notes that I've seen for the P53 and the workstation dock (very poor grammar, hard to understand to the point of almost saying "something changed") I'm feeling dissapointed with Lenovo. I know the history of the company, I've started with an IBM Thinkpad 18 years ago and have had others since, but I was hoping that at least the professional models would see traditional attention to detail. I mean, Dell also has sharp edged laptops with trackpoints for professional use, if you know what I'm saying.
*- because laptop manufacturers are known to lie about compatibility in regards to RAM and storage. "only what we sell is compatible, nothing else is guaranteed to work", even though we're talking about parts that meet the required standards. See also the Workstation dock, which they sell in 3 SKUs and one is not listed as compatible with the P53 despite the only difference being the AC adapter that's in the box, as if you couldn't plug in your 170W or 230W adapter and achieve the same result.