Best balanced linestage/preamp for $4000 or less ???

You've conveyed features you want in a preamp, but you haven't mentioned anything about what sound characteristics are most important to you or what you'd like to improve upon over what you have currently.  You'll get much better recommendations here if you can share that info as well. 

I was going to suggest a used Atma-Sphere MP-3, as Charles did, except that I’m pretty certain it only provides a single pair of XLR outputs, and no RCA outputs, at least in its standard configuration. If you can find one that you would want to consider, though, a call or email to Ralph Karsten at Atma-Sphere would be in order, to see if he could modify it to meet your requirements.

Many of the other suggestions that have been made also will not meet your stated connectivity requirements. In addition, many tube-based preamps (NOT including Atma-Sphere’s) will have problems driving the line-level input impedances of many and probably most powered subwoofers. Line-level input impedances of most (although not all) powered subs tend to be in the range of 5K to 20K or so. 20K is the lower limit of the load impedance ARC recommends for most of its line stages and preamps. Also, many line stages and preamps made by ARC and other companies drive their RCA output connectors with the same signal that is provided to one of the two signal pins on their XLR output connectors. Which means that the output stage providing that signal would be loaded by the input impedances of BOTH the sub and the main power amp, and the input impedance of the sub may therefore affect the signals received by the main power amp. In this case your power amp fortunately has a high input impedance (100K), but even so 100K in parallel with 20K would result in the preamp seeing a load impedance of only 16.67K. And 100K in parallel with 10K would result in a load impedance of only 9K.

I would have significant concern about BAT preamps as well (many of which would require, btw, that you use an adapter or transformer to convert balanced outputs to single-ended, to drive the sub). For example, while the VK-50SE has a specified output impedance of 200 ohms, presumably based on a mid-range frequency, Stereophile measured its output impedance as rising to 4600 ohms(!) at 20 Hz, which would make it unsuitable for use in driving a sub having a typically low input impedance. And the corresponding numbers Stereophile measured for the Aesthetix Calypso were not a great deal better.

I have no knowledge concerning the Backert preamps, but based on a quick look at the other tube-based models that have been suggested the only one that I suspect might meet all of your connectivity, functionality, and drive requirements is the Freya!

Good luck. Regards,
-- Al

Asking $3600, but pickup only

@almarg  ..  would finding a preamp with direct coupled outputs solve this issue ? The MP-3 MK3 is designed this way and I see some other preamps heading this way..