Help with speaker cable under $500 for new system

I would not worry about lower DF. Inductor in series with the woofer has resistance in order of 0.1 ohm limiting DF to 80 anyway, not to mention that speaker's own impedance is mostly resistive. Even 4 ohms would make DF=2. Additional resistance in series shouldn't contribute much. Less than 10% would be ideal (0.4ohm). I would worry more about reactive inductance of the cable at high frequencies (higher for thinner cables). Assuming 0.4uH/ft your 12' cable would have (both ways) 24ft x 0.4uH = 9.6uH. Reactive impedance at 20kHz would be 1.2ohm. On the other hand tweeter's impedance can be pretty high at 20kHz making it unimportant.

I'm using Acoustic Zen Satori. Silky smooth and fast. It should be within your budget (used).

Al, 23 gauge copper is not that different (0.489 ohms).
Damping factor of 14 is OK since, as I mentioned, speaker
itself limits it to <2. Atmasphere amplifiers have DF<1 and
are highly praised.

I'm not sure how significant difference in colorations would
be between DF=2 and DF=1.8

Choice of higher gauge might be more practical - 23 gauge is
fragile to work with. Also, there might be cables much
longer than 12ft where it will start playing role.

My cables have very weird construction with multiple wires
on huge hollow tube. My suspicion is that they want heavy
gauge to reduce inductive reactance but at the same time
split wires to avoid smearing by skin effect that starts at
about 18ga/20kHz. Stranding itself wouldn't help since
current would jump from strand to strand (bad) to outside
while insulating strands helps a little, but they are still
in magnetic field of each other. Possible solution is to
place them on the hollow tube - so that they are in magnetic
field only of the neighboring strands, or weave them into
flat tape (for the same reason). It is all black magic, but
at least I can see what they are trying to achieve. What
puzzles me is presence of one single strand that is
insulated but stranded again inside (10 tiny strands).
Going by engineering principles would make us to buy only a
lamp cord from Home Depot :)

Al, I agree but since source/speaker resistive impedance is likely at least 50% of nominal impedance (perhaps 2/3?) making best overall DF you can achieve equal 2. I would avoid using anything that can lower it further but additional 0.5 ohm would lower DF only by 12.5%. - all assuming that amplifier doesn't contribute anything.

Of course we assume that lower DF effects will be, if anything, negative, while in many cases (overdamped speakers) is perhaps the opposite. We often claim that low source impedance (voltage source) is the best, but then we enjoy higher output impedance (power source) of tube amps.

High DF chasing might not only exclude great cables but also promote selection of poor sounding amps with deep NFB.