I designed and built a handful of inductor-based phono stages about fifteen years ago, both tube and solid-state. I used pre-made LCR networks from Tango and S&B (both now out of production), and a couple of LCR and LR networks of my own design with inductors custom-wound by Sowter. And while I certainly have no inherent prejudice against inductive components in the signal path, I ultimately felt that it wasn't the best way to go . . . but I'll share a few of the conclusions (at least that I can remember).
As others have pointed out, designing the network to a lower impedance reduces the inductor values and makes them easier to wind, but it at the same time pushes the inductors' ultrasonic self-resonance frequency higher, and further from the audioband. The Tango and S&B units I had were both 600 ohms, and one of my Sowter-based networks was significantly higher (about 2K IIRC), and the latter's transient response was poorer in an immediately obvious way, even though the RIAA response through the audioband was at least as good.
The other impedance idiosyncrasy (not surprisingly) about all the networks was that distortion was markedly lower when driven by a zero-impedance source, and terminated by its characteristic impedance, rather with "equal" impedances at each end. The noise figure is obviously lower as well. It also seems that the better the winding techniques and core materials are, the more sensitive the inductor is to any amount of DC current leakage. So I'll admit that I'm scratching my head a bit as to why LCR equalization and (especially low-feedback) tube electronics seem to be frequently associated, as the "impedance comfort zones" of LCRs and tubes don't much overlap, and some traditional tube biasing techniques that put DC through the inductor are definitely a no-no with a precision LCR EQ network.
If you load the input stage cascode with an active current source you can effectively achieve an infinite output impedance. This allows you switch the RIAA series resistor from a series connection to a shunt connection. No issue with RIAA response changing as the tube ages. The excess current from the plate load CCS is shunted across this resistor to ground and sets the plate voltage. Neat trick. To maintain the set plate voltage the cascode pair needs to be biased with a cathode/source (tube or tube/SS hybrid cascode) CCS.
As I read it, the operating conditions you describe are identical to a conventional transconductance amplifier with a plate-load resistor to B+. To the audio signal, the load resistor goes to ground either way, it's just that in the traditional topology the current is capacitively coupled to ground through the B+ supply capacitor. The source impedance is still the tube's output impedance in parallel with the load resistor, and since this resistor loads the signal, its value is still the limiting factor for the open-loop gain. Just because there's a constant-current-source yanking the DC parameters into submission doesn't change any of this; rather, is simply adds one more uncorrelated noise source to the equation. Maybe I'm not seeing something fundamental about your circuit description, but (no offense) I don't get how this is any kind of improvement over the basic tube circuits of seventy years ago.
But this does highlight how many designers make broad topology decisions in conjunction with their approach to RIAA EQ . . . so in evaluating various designs, it's hard to know what are the characteristics of the LCR approach in general, and what's simply the sonic signature of the circuit design as a whole. Incidentally, my favorite of the tube designs from the aforementioned exercise was five tube stages from three tubes per channel: WE417 followed by 12AT7 (both plate-loaded) and a 12AX7 cathode-follower, with global NFB around these three for a very low output impedance. I then used the Tango iron loaded at 600 ohms, and then the other sections of the 12AT7 and 12AX7 (also plate-loaded and cathode-follower, respectively, and with global NFB around the two) as additional gain and buffer. Sounded great especially with an MM cartridge.
My favorite solid-state approach was two 990 opamps, the first one giving active 318uS and 3180uS EQ and driving a LR network (IIRC 200 ohms or so) for 75uS EQ, then the second for additional gain and an output buffer. This was better for MC cartridges, especially when I added a Jensen 346-AX input transformer for a bit more gain, and so could reduce the electronic gain of the first stage.
At some point I removed the LR network from the SS preamp and substituted an RC . . . and found I liked it better. I recall the RIAA tolerances for the LCR-based units to be better than +/- 1/4dB or so, the RC/LR design was significantly tighter as there are fewer interactions, that is the resistor values can be easily twiddled to match the inductors and caps. The S&B units seemed to have a bit of an ultrasonic peak that I tamed down with a small-value Zobel network - the same approach wasn't completely successful with the higher-impedance LCR network.