No problem using the #12 THHN Stranded for Speaker Leads.
Would be a good idea to "Tin" the ends, so they fit solidly and cleanly to the Terminals at the Speakers and the Power Amp.
Do this by applying Solder to newly stripped ends of each Conductor.
As to the zip ties, feel free to use them.
You could also bundle a pair of leads with small segments of Electrical Tape, at 12" intervals (costs less than zip ties).
Keep the bundles separate (only bundle the 2 wires for a given channel), however, you may run bundles "together" (near each other).
Additional Audio lead tweeks may be employed, depending on how far you want to go - and the output power of the Power Amp.
As said previously, the #12 THHN Stranded will work fine for Audio Speaker leads, as long as your Power Amp is not something capable of delivering a huge level of Power to the Loudspeakers.
If your Audio Amp does not exceed 100 Watts per channel output (into an equivalent quoted Impedance), and the leads are not too long (Amp is in the Garage, Speakers are in the Master Bedroom...overboard example), then the #12 is fine.
Higher Power levels would need larger Conductor sizes, or "Parallel-Lead" techniques.
FYI: "Parallel-Lead" = Running separate pairs of "+" and "-" leads to each Speaker Enclosure, with a "Dedicated" Pair for the Subwoofer, and another "Dedicated" Pair for the Midrange + Tweeter (or a pair to each driver).
Reconfiguring the Crossover's inputs is needed at each Speaker.