I don't know if I understand you very well, the heater regulator is DC LM317.
It does not matter what your heater regulator is. Heater MUST BE AC grounded.
I don't use feedback, see attached schematic.
That circuit should run a single triode of 5687WB, not two in parallel. Current will be around 10mA per channel.
Place a 3.3MOhm resistor in parallel with the battery. Personally I would also add a 10nF silver Mica or C0G ceramic capacitor.
This circuit has a bit more PSRR than what I referred to earlier at around 12dB, still, noise on the +B will bleed into the audio circuit.
If using a 100k Pot, make sure to use well shielded, but low capacitance cable for connections, I tend to make my own using PE (never PTFE) tubing, Silver Wire & copper braid.
As this circuit still has 22 dB gain possible options are to get something more usable are:
1) Arthur Loesch / First Audio Presence style - place a 10K attenuator on the output, first it drops gain to 20dB and you attenuate tube noise along with all the rest. For 2V standard inputs I tended to use a voltage divider on the input, to lower gain to around 8dB (so 4:1 attenuation - e.g. 33k/11k - in practice 33k/10k) while also having some higher gain inputs and of course a Phono stage. In these preamp's I implemented a neat trick, using the tube heater for input switching - as I only had two sources (LP & DAC) this worked splendidly using one tube per channel...
2) Jim Fosgate / Thorsten Loesch style - place a 680k resistor from output to input (before the battery, not tube grid in your case) and a 100k resistor in series between input and attenuator. Now you have around 8dB Gain using local feedback (single stage) which lowers noise, distortion and output impedance, the way feedback does. The around 14dB feedback work quite well, with a Z out around 600 Ohm in practice.
Either way works, I tend to prefer #2 nowadays, but it is a matter of taste.