I'd be curious what you might like in the $1000 range, if anythingI could not presume to assume even in the $10 range. As mentioned, I use Transparent interconnects and have heard excellent sounding systems with Transparent, MIT, Monster and other manufacturers' speaker cables. I've also heard some bloody awful ones with those, AudioQuest, Nordost, etc. I've also heard systems with homebrew cables targeted to amp and speakers that were just gorgeous.
BUT, and it's a BUG BUT, I'd only voice an opinion after an in situ listen.
I have no knowledge of the A3s, the amp, the room, the table / cartridge and, most of all, you.
Cost is no arbiter of performance and many designs are just plain bad from an electrical perspective of getting an undistorted signal to the loudspeaker. They may improve some aspects at the expense of others. Rarely, if ever, will anything be exactly right everywhere on a particular system.
Some designs may work exceedingly well with a small subset of amplifiers and speakers, failing miserably on others.
Many years ago, I happened on chap receiving a 'lesson' on why the item on demo was 'superior.' He seemed a tad bewildered and off-handedly asked what I thought.
I said "I don't think it sounds at all like it was recorded."
Annoyed, the salesperson asked snottily "And just how would you know?"
"Well, it just so happens I recorded and mixed it" and then showed him my driver's license to counter his expletive.
The chap then asked what I would recommend and I told him I would have to learn his peccadilloes and hear his present system before I could possibly even comment.