I've had trouble with the Inserts Lowe's sells, too. They're too flimsy, as you've found, at least for hardwood.
I get mine from
McMaster-Carr. I've used both brass and stainless to good effect, but prefer the stainless any more.
The inserts look like this...
It has an 8-32 internal thread and requires a 1/4" pilot hole.
The brass P/N is
90016A009 and they cost $8.79/pkg. (25 parts)
The SS P/N is
95807A100 and they cost $2.80 each.
In either case, you need a power driver. Trust me, you'll
never pull this off with a screwdriver. With wood as hard as necks are made of, the insert will fight you tooth, fang and claw, even with the tool. You'll need a variable speed drill motor as well. The tool looks like this...
It's their P/N
94110A120 and it costs $9.26.
For screws, you want some philips oval head SS machine screws. Depending on whether you've got a standard or contoured body, and whether you've had the "720 mod" done to it, the screws need to be 8-32 x 1 1/4", 1 1/2", or 1 3/4".
They look like this...
1 1/4"
91802A201 $9.06/100
1 1/2"
91802A203 $7.08/50
1 3/4"
91802A204 $7.60/50
I
strongly recommend you use a drill press for the holes. They need to be perfectly perpendicular to the neck, and you have to be ultra-careful you don't drill too deep and run into fretboard.
Also, when running them in, be sure to wax the threads and run the drill motor
very slowly with plenty of down pressure on the part. As I mentioned earlier, they're going to fight you.
If you want to avoid the fight, you can pre-thread the hole with a bottoming tap. I recently started doing this, and it works well. It's an odd-sized tap, though, so finding it locally may not be easy. For these parts, it's a 5/16-18
bottoming tap. Using the tap also prevents the blistering Mayfly mentioned.