If you're still having trouble, what if you slip the three stitches onto a thinner needle (or anything thin for that matter than you can knit from, if you don't have extra needles), and doing the k3tog from that? Unless you're using like, size US 0 needles, you should be able to find SOMETHING small to put the stitches on.
If that doesn't work, I give another vote to KP needles! They're not any more expensive than the Bates needles at Joanns (I don't know what Walmarts prices are), plus a bit of shipping, and a few days wait. But they are so completely worth it.
You'll want to be cautious though, since it sounds like you're a really tight knitter, so you probably do a lot of re-adjusting the stitches/needles by pushing the needle tips down with your fingers right (or am I the only one that does this? lol)? If you do this, then there might be a bit of trouble with sharper needles because they're, well, really sharp! I got used to it really quickly though, like within a few stitches.
The looser you actually knit (not just cast on), the easier it is to knit the stitches. Try not tugging the yarn as much after each stitch, and see if that helps at all.