Thanks! I guess I can try again. I rented a drill for $75. Used it for 1 hour and barely got the hole started. I got the 3 inch bit with the drill and a chisel as well. The hole is in a tight spot and I forgot to get earplugs. VERY important to get plugs! I literally couldn't keep drilling in the spot and not have my ears hurt. After seeing the concrete was several inches thick, I gave up and thought I'd get a 'specialist' to take care of it. I still haven't gotten past the concrete surface. I figured they would have a specialized tool or something. I may try again (with earplugs!)on my own someday. I just thought if it were cheap enough, I'd get it done by someone else. thanks again.

Those are great questions, grubby_me! It never occurred to me it could be a conduit based on how smoothly it seemed to transition from one material to the next, but it's definitely worth looking into in case it actually is a conduit. Other ways I can think of getting into the joist space are: 1. Through the roof. I'd rather not try this, especially since I'm relatively inexperienced with this type of work. 2. Through the ceiling of the room beneath. I opted for the external option because I figured those chambers could use ventilation. Cutting holes that lead into the room beneath would just ventilate the hot "attic" air into the bedroom. I'll see if I can get some pics. Hard to get good pics of the bottom of a narrow hole. :oP I'll see if there's anything else I can take pics of that might give clues of what I'm drilling into...

As someone with experience in asbestos removal, I can say that vinyl asbestos tiles often become brittle over many years, and can fracture into a lot of pieces when you're trying to remove them. The Minnesota Dept. of Health web site has a lot of good info, but the assumption that one can "work under the edges of the tile and pop it loose" is not correct in some cases, especially where one is dealing with old tiles held tenaciously by black mastic. Old vinyl tiles are not like the "peel and stick varieties. We don't know how old the OP's tiles are, and, even if we did, the approach to such a situation can vary from site to site. I'm not trying to get in an argument over removal techniques, or say there is only one way to deal with this situation. But I am pointing out that slowly drilling some holes in vinyl tile with an encapsulant capturing stray fibers may be a better approach than thinking you can easily pop up some tiles. This is a case where one could try to remove tiles, end up fracturing them into multiple pieces, scraping at the mastic, and having a mess on your hands. I'm not holding myself out as an expert. I'm counseling the OP to look at a low-tech approach that may result in less risk compared to trying to do a "better" job by removing tiles.

We are still in progress, so I can't post actual pictures yet, but here's a drawing of what we're planning (top down view and front view). Where the beam actually ends up falling lines up pretty close to right beside the range/microwave. So, The rest of the cabinets go to the ceiling, but that one we made the whole width available to the corner, but made it only go up to the beam. Then in the void beside the beam, we're putting a little "dummy" cabinet. I asked him if there was a way to actually make the "dummy" door functional and leave it open behind there so that we had the space to put something there if we want, since the kitchen isn't very big, and he's going to try to do that. I'll try to remember to post pictures when it's all done!