Are you sure you have his current contact info? People change phones and lose email accounts all the time, so start by making sure A) You have good, current contact info, and B) Your messages are getting through.
My phone sometimes tells me it sent a text, when it didn't, and I routinely have my emails end up in people's spam folders, so keep that sort of thing in mind.
This depends on a lot of factors. Generally, if the money isn't a huge deal, lawsuits are more trouble and stress than they're worth. Then again, sometimes emotional satisfaction is worth the trouble, and this sounds like a small claims case, which isn't quite as involved as other types of lawsuits. Keep in mind that even if you win a court case, you still have to collect the judgment, which can itself be pretty difficult sometimes.
I would definitely not do this until after consulting an attorney on this issue. I can see a ton of ways this could backfire. This also "wastes a bullet," so to speak, and will make your attorney's life more difficult, not to mention how other cue makers may feel about a guy who might call the cops on them if they make a mistake.
This may make some sense if he just isn't getting your messages, but again I can see a ton of ways this could have a bad result, and there are probably easier ways to make contact. If you're OK with flying to him, small claims court might make more sense.
Are you sure he hasn't broken your cue, or lost it?
If this is important to you, I'd suggest reviewing EXACTLY what has happened - what was discussed in terms of timelines, difficulty of repair/replacement, etc. Did you say, "Just do your best - it might not be repairable," etc.? What can you *prove* in terms of the cue's value, repairability, what was promised, how many times you reminded him about it, etc.? What do you have in writing?
If you take the most critical look at yourself, did you do anything that might put you at fault, at least a little bit?
Once you have that straight, and are certain he is receiving your messages, I'd start with, "I understand if something went wrong with my cue, but that cue meant a lot to me/was expensive/(whatever). I really just want it back, and you don't even have to do the job I asked for originally, but if that's impossible, where can we go from here? I'd like to work this out." You must like the guys' work, so maybe he has something to offer you, if you're cool to him.
If he provided you any receipt, include it - he might not even remember something from three years ago. Also a picture of the cue might help.
If that fails, I'd go with, "I really don't want to get an attorney involved, but I don't know what else to do. I just want my cue back, and I'm open to talking over what you might be able to offer me, in case you've lost the cue, or whatever."
Only if that fails would I get an attorney, and you have to think out beforehand how far you want to take things. Attorneys can be rough to deal with, and best case scenario you'd pay $300-$500 (or more) for a threatening letter and a couple phone calls to the cue maker. If that doesn't work, my best guess is you'd take it to small claims court, and deal with various court rules (e.g. if you're an LLC, you might need to have a lawyer represent you, depending on the rules of that jurisdiction).
I might tell you "Don't bother with a lawyer - just take it to small claims yourself," but after you said you are thinking of confronting him personally and/or calling the police, I strongly suggest you talk to an attorney before doing anything aggressive, because those things could backfire in a myriad of ways, and being ultra-aggressive like that will look bad to almost any judge - if it does go to court, you want to be able to prove that you sent him a valuable cue, he agreed to repair it, you tried to work with him, and he's the one being a total jerk.
Of course, if you have the resources, you could just have a gang of hoodlums raid his shop and take all of his equipment, and also seize his children to be sold to a human trafficker, but there are downsides to that approach, and I recommend against it.
(Disclaimer: None of this is legal advice, and if I am an attorney, I'm a weird one who isn't authorized to practice law in your jurisdiction. Nothing I post on this site should be construed to form an attorney-client relationship with anyone, even myself).