The problem is that your 15K:600 transformer is designed to go into a 15W power amp and to take 100mA of DC current.
If you're going to load the 5687 with a CCS and take the DC current out of the output transformer, you will get a huge increase in performance by using a different (smaller and less expensive) output transformer.
If I have to change transformers, what about these amorphous 5k 300-600ohms 2W 50mA CC: Transformador de salida de doble nucleo amorfo C 5K de un solo extremo para 300 600 ohm auriculares delanteros, potencia de salida de aproximadamente 2 W, mas de 50 mA CC|Transformadores| - AliExpress
If you are going to use a CCS to load the tube, do not buy a gapped output transformer. The one you linked to says "50mA", so it is not what you want.
I modificated one of the completed parafeed preamp schematic.
Now I don't have 15k:600 transformer parameters (only 10k and 25k was modelled).
If you have (besides that you already measured) another parameters of transformer:
Cip: primary coil capacitance (preferably at 10-100kHz);
Lsp: leakage inductance (measured primary inductance, when secondary shorted);
the modelling is possible.
It's not enough.
Cip and Lsp is mandatory.
I guessed these parameters.
I'm not sure, that secondary inductance is correct value. If it's 15k:600 transformer, the secondary inductance rather 0.48H than 0.38H.
This simulation HF behaviour is uncertain without missing (but guessed) parameters.
At this case of low primary inductance (12H) designing of the parafeed circuit is very frustrating, the parafeed capacitor value is go to the sky.
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