As I understand it, when driving loads over a long distance, what you want is a high-current buffer/driver. It is
both the low output impedance, plus the higher current drive, that serves to overcome the cable capacitance.
Think of it this way. In a conventional single-pole lowpass filter like this:
The cable provides a series resistance, and also capacitance between the conductor and the shield. If the distance is short - as in a 1/4W resistor and capacitor - the formula for identifying where the high-end rolls off is given by 1 / (2 * pi * R *C), where R is megohms and C is in microfarads. If R = 10k and C = .01uf, then those two components roll off frequencies above 1591hz at 6db/octave. The cable you will use to connect the open-reel machine and the rest of your system, also has a linear resistance, and a linear capacitance (i.e., both increase the longer the cable).
The rolloff is partly dictated by how fast the resistor/resistance permits charging up the capacitor. Since the resistor is in the series path of the signal, and higher resistance reduces how much current can pass, increasing the resistance lowers how much current is available to charge up the cap, lowering the rolloff (e.g., if R = 100k in our example, rolloff begins around 159hz).
Working the other way, though, if the resistance is fixed, then trying to pass
more current through that same resistance allows the cap to charge up faster, and so results in less high-frequency loss. That is, the resistance will reduce current flow from whatever you started out with. But if you start out with more, then more gets through.
So, since you can't do much about the linear resistance of a cable connecting the tape machine in one part of the house, and where you're running the signal to. And since you can't reduce the cable capacitance (apart from using the lowest capacitance able you can find), then the next best thing is to use a lot of current drive to send the signal over that cable.
There are different ways of achieving that. One of the simpler ways is simply to parallel stages. My buddy Jack Orman has a simple project for a "super buffer", intended to address this very problem:
AMZ Super Buffer for Guitars
Filters at work prevent me from linking to the schematic, but you can see that it consists of 4 paralleled versions of the exact same buffer stage. Their combined current output allows for it to drive a very long cable. This is the sort of thing one might use for feeding a mixer 100ft back from the stage to a power amp right in front of the stage. There may be other sorts of devices, for example those that use transformers, but this is cheap and simple, and small.