According to the specs shown
here the Parks Audio Budgie phono stage has an extremely high specified nominal output impedance of 6,000 ohms. And I wouldn’t be surprised if that value is even considerably higher at some frequencies. (Although I’m a little uncertain concerning your use of the word "hybrid" in referring to it; is your phono stage a different configuration than what is shown at the link, which is described as having an all tube signal path?).
Assuming that none of your cables or power cords are especially long, and assuming the 6,000 ohm spec is applicable to your unit, I would therefore think it likely that the connection of the phono stage to the integrated amp would exhibit greater sensitivity to cable (or power cord) differences than any other connection in the system.
Although that is not to say that you would necessarily find a given $500 pair of cables used at that location to be subjectively preferable to the Blue Jeans you are using now. And in fact low capacitance, such as Blue Jeans LC-1 provides, assumes particular importance when a cable is driven by such a high impedance. But as I say I would think that interconnection is likely to be the most cable-sensitive point in the system, and it is therefore what I would focus on first.
Good luck. Regards,
-- Al
