Tom,
You're seeing why I have settled on eSATA for these projects. My eSATA external drives are on the SATA bus.... just as much as an internal SATA drive. There are cables that let you have eSATA plug on one end and the female normal SATA on the other, so if my workstation has an eSATA port on the backplane then I can directly connect a bare SATA SSD or HDD to the SATA bus, with use of an external power supply, fed to the HDD or SSD SATA power connector. For this type of work you want to use a short high quality cable.... Or, I use a high quality external eSATA drive case from OWC or G-Drive and a Molex brand eSATA to eSATA cable.
Your old driver is a USB driver.... that is not the issue. For SSDs on modern OS such as W7 and on you don't need a special driver..... the OS install will have what you need in reserve. The Intel ToolBox is a SSD utility.... current version is 3.3.3, and you can tune up your SSD install some with that, run TRIM, and update firmware easily.
If you look at the rear end of a HDD or a SSD you'll see that the interfaces there are male SATA data and male SATA power. What they mate to is usually a SATA interconnect cable, which has female on each end, and the SATA port on the motherboard usually is male too. With the Foxconn BlindMate interface that HP uses in your Z1 and in the rear end of the drawers for the Z620, etc, is a female connector for both power and data.
Hence, the SSD's male end can plug directly into that female BlindMate receiver. This means that you'd need a SATA extension cable to try to get the SATA data port fed outside of the Z1.... male on one end (to plug into the BlindMate SATA data part) and female other end (to plug into the rear of the SSD).
Those exist.... I have looked that up, but have never needed to buy one.
Regarding using an external source of power rather than getting the power to the SSD from the Z1 itself. I have used external power supplies for exactly this purpose for years now, and with never a problem.
Scott
p.s. I can tell you that by now I'd have done a clean install from scratch. However, have done that at least 500 times over the last 8 years on my projects here, so it is pretty much auto-pilot. I had to start from ground zero over and over to finally figure out some patterns that failed and worked.