Why not try a BAT VK3i? It's fully balanced in and out and also has RCA in and out, w HT pass thru. It has remote volume and input selection (optional, but most have it) and would a used one would be at the lower end of your price range. BAT has great service.
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Just today, there are two Pass Labs pre amps listed, one the single chassis and the other is the two piece. Both are within your range. The way the pass works is to have all signals balanced, check this at the pass site, even the rca are treated as balanced once in the circuit. i love mine, and have had the BAT, Placette, and several others. Will drive the distances you want.
Yes, your approach sounds quite reasonable to me.
I second Shadorne's suggestion of the Benchmark DAC1 Pre (or HDR if you need remote volume). Depending on your source, you'll get an upgrade there for free.
I can recommend Belden 1800F STP cables (13 pF/ft).
Keep in mind that the preamp you choose should have low output impedance, and the cabling you choose should have low capacitance (such as the Blue Jeans cables Bob suggested).
Balanced connections do not negate the possibility that high output impedance in combination with high cable capacitance (which is proportional to length) will roll off the upper treble. At least some of the BAT preamps, and some of the Pass Labs preamps, have worrisomely high output impedances in that respect (e.g. 750 to 1000 ohms). The Ayre should be fine, as should the Benchmark for at least some of its output attenuator settings.
You might be able to find an ARC Ref 1 line stage which, IIRC, had the lowest output impedence of any ARC preamp. Very high sound and build quality with bal/se capability and (if you're lucky) a manageable price tag on the used market.
Al - "worrisomely"? Cool word, but at least one too many syllables for daily use.