Best place would be right back to Shimano, reason I say that is it may be difficult to get specific wear parts and they would have them on the shelf. I think they do a complete rebuild for around $30, but not sure if that still applies.
I’m in the same situation with old 500/600’s. I sent one back 4 weeks ago to shimano and still haven’t heard anything. I read somewhere it was a 4 to 6 week turnaround sending back to Shimano when I sent mine in. My guess is it could be longer now.
One common problem with the 500 and 600 Tekotas is the anti-reverse bearing which is a real bugger to remove and replace. Shimano apparently has a special way to remove this bearing. In my shop I too often have to resort to the Dremel. That works but I hate to do it. Send your reels to Shimano.