The issue of "best possible" is something that we all ultimately chase but such success comes with a lot of experimentation, personal choice and compromise. And once we feel we have this, along comes another "best" component to make us no longer content with what we have.
I agree with Bob's advice here to seriously consider separate line and phono stages. A full function preamp like the CAT or the Steelhead may be a good starting point. And then you can experiment with other separate line and phono stages.
As an owner of the JL-3's, the mono version of the JL-2, the one thing that I paid dearly for with these amps was their dynamic and resolving capabilities. Careful selection of upstream products that might limit these strengths, as Bob wrote with the Steelhead directly driving his amps, would be something I would pay much attention to.
I tend to like a very large 3-dimensional presentation, volume of space portrayed, decays, image size, etc., so my attention has been here for many years. With the CAT amps, hearing their strengths and a much more neutral presentation brought me a little closer to center. But my gut feeling is that the CAT preamp would go too far toward an analytical sounding presentation for my own personal taste. The key is to find a system balance between the one side of resolution, dynamics and neutrality and the other of space and dimensionality.
I have found the Aesthetix Callisto/Io combination to be an incredible match with the JL-3's. This is over your $7500 budget but the Io can be configured with volume controls and such a used unit does fit in your budget; they simply are not for sale too often. Audiogon member Rushton has much experience with the Io Signature with volume controls. Hunt down some of his posts as I suspect this might be worthy of your consideration.
John