One more cable plus transformer - this will degrade the sound. Separate phono with appropriate output impedance will be better. What is the good range of output/input impedance proportion, 1/5-1/10 or so ?Ideally 1:10 or better is the rule of thumb.
It will be tricky to come up with a tube phono section that is OK driving 10K ohms. While the output impedance might look low enough on paper, the defining spec is what the output impedance is at 20Hz, not 1KHz.
That is why I recommended the transformers. BTW, input and output transformers are quite common in studio gear, from whence most of our recordings come. I don't like transformers, but they have their place and when they are needed, they can be really helpful!
Where will the extra cable be used??