tzrider builds his own wooden furniture out of native trees. He has dealt with burrowing bugs in his own creations. He might have some suggestions
Thanks for the vote of confidence, guys.
As a hobby, I do build rustic furniture from trees I felled. Some of the trees have been standing dead for a few years and have contained small borers of some kind.
The bad news for you is that, it being rustic furniture, I haven't really worried about borers in the wood on the few occasions they've been present. Bore holes typically already exist in some of the wood I select, so I figure what's a few more? It does seem that the larvae die on their own after the furniture has been indoors for a while. It may take a couple of years, but without moisture, eventually they die out.
If you need them dead before they make your non-rustic furniture look like it came from Jed Clampett's house, the link Owensdad posted might help. If there is an exposed borehole, you may be able to kill then by directing insecticide into the hole itself.
Two years ago, I carved an outdoor bench out of a log that was seriously bug eaten. Gave it "character," I thought. There was a large bore hole in one surface that I'd been sanding. After I sanded for a while, I'd take a leaf blower and blow the wood clean so I could tell how much more sanding it needed.
I was inspecting one area and then turned towards the bore hole which had been totally clean three minutes earlier. There was now a pile of sawdust outside of it. Figuring I was mistaken that I'd cleaned out the hole, I hit it with the blower. A few minutes later, the sawdust was back.
It was a big hole, about 5/8" diameter. It was obvious something was going to town in there. I didn't have any insecticide, but I had some mineral spirits and poured a bunch all over the bench and down that hole. I thought, "Take that, fucker."
An hour later, I brought my wife up to see how the bench was shaping up. When we got there, I looked at the bore hole and saw the tip of a larva that was as big as the tip of my forefinger. The bore hole was still pooling mineral spirits and the larva was partially immersed in it. My wife thought it was cool and tried to coax it out. She finally got it out without crushing it and the thing was fully the size of my forefinger in length too! And it was alive.
She brought it in the house, because her sister was due for a visit that night and we thought showing her a freak giant grub would be a nice surprise. It was; my sister-in-law was very surprised. :laughing
After we got her and her husband off the ceiling, we decided the keep the thing so that we might see what it became. Mind you, this creature was going strong after being drenched in mineral spirits for an hour. I got a couple of bags of sawdust from the same tree the larva had been in and we kept the thing. It lived at home for about 8 months before it finally expired. We learned that they can live for a number of years before maturing into a beetle (rhinoceros beetle, in this case). Evidently, a pile of sawdust is not a satisfactory environment for something that prefers to bore into and kill live trees, but we tried.
This little anecdote may not be incredibly helpful to you other than to illustrate how resilient these creatures are. If you don't want to face the possibility of having more bore holes appear and don't wish to periodically clean up little deposits of something that looks like sawdust, but is really larva poop, I'd suggest a general insecticide that works on beetles.