As someone who faces similar search troubles when designing electrolytics into new designs, I feel your pain....
Sorting by ascending ripple current on Digi-Key quickly turned up the EEU-EB1A222 as a reasonable candidate for you. (There may be better choices; that's just the first one I found.) As well, physically smaller capacitors are often forced to have higher ESRs due to their construction, so don't limit yourself to a single size if smaller parts might fit.
(Aside: those measurements look a bit fishy. In particular, I am suspicious of those high Q values for electrolytics; you may want to check your meter. But that has no bearing on your main point.)
Thank you for your honest and experienced opinion. I appreciate the specific capacitor recommendation very much indeed, and found it in stock on Mouser as well:
https://www.mouser.jp/ProductDetail/Panasonic/EEU-EB1A222?qs=sGAEpiMZZMtZ1n0r9vR22RyzzjEKRzqKYIaKulH23zw%3DDF@120Hz is a fairly high 0.32 (a good thing in this case), and the rather low 540mA Ripple Current spec indicates the ESR is rather high (also a good thing, I think, as it more resembles what the stock cap was probably like back in the day). And yet it's rated at 105°C and for 10,000hrs, and from a well respected maker of aluminum electrolytic, making that cap a wonderful pick, in theory. I will purchase it and put the theory to the test.
By the way, here are photos of the PSU inside the HD20SC drive enclosure, and the bottom photo clearly shows the 10V 2200uF Rubycon I've been talking about. The beep sound, to my ears, comes from the area of those two transformers nearest to the cap:
https://www.icloud.com/sharedalbum/#B0wGQOeMmGzwJPAAnd here is the full list of caps showing the stock capacitance, voltage spec, physical size and lead spacing, with my replacement capacitor part number shown in parenthesis at right:
C226: 22uF 35V, D=5.2mm, Leads=5mm -- (Mouser: UHE1H220MDD1TD)
C202: 47uF 25V, D=5.2mm, Leads=5mm -- (Mouser: EEU-FR1E470B)
C222: 47uF 25V, D=5.2mm, Leads=5mm -- (same p/n as C202)
C109: 150uF 400V, H=32mm, D=25.8mm, Leaders s=10mm -- (Mouser: 860021383023)
C110: 4.7uF 350V H=32mm, D=12.8mm, Leads=5mm -- (Same as SONY C164 - Mouser: UPM2G4R7MHD)
C210: 330uF 16V, D=8.1mm, Leads=5mm -- (Mouser: EEU-FR1E331B)
C215: 470uF 10V, D=8.1mm, Leads=5mm -- (Mouser: EEU-FR1E471YB)
C213: 22uF 100V, D=10.2mm, Leads=5mm -- (Mouser: UBT2A220MPD1TD)
C214: 2200uF 10V, D=12.7mm, Leads=5mm -- (Mouser: UHE1C222MHD1TO) <-- the problem guy!
C209: 2200uF 16V, D=12.7mm, H=30mm, Leads=5mm -- (same p/n as C214)
I knew I needed a "16V" 2200uF cap for C209, so I thought it no harm in going with the same cap for C214 too, but that wasn't a good assumption.
Anyway, I took measurements more than once with my DE-5000 to make sure of the accuracy. It took several minutes for the DF value to settle though. It kept rising and rising. But the biggest frustration with this meter is that it won't show me enough ESR info at 100Hz or 120Hz. The tenths place isn't enough. I want to see down to 1mΩ! I can see that on smaller capacitance caps which allow me to crank up the test frequency, but this large capacitance caps don't let me use anything higher than 120Hz.