I like your approach, but the total depth of focus for a 35mm, 10x enlargement at f/5.6 is about 0.5 mm. A 2x enlargement of an 8x10 negative is about 0.7 mm at the same aperture. A little heat from the light source and the negative will 'pop' out of focus. A glass carrier is the only way to hold a negative flat.
I agree with all that. Sometimes, when I'm in a hurry or doing shots of the kids or something, I don't want to use the glass carrier with 35mm. I'll measure my delta v on the enlarger column ( the distance the head needs to be moved up or down from the high to the low point on the negative). I punch that number into the focusing equation and have good results at f11 or f16. The key is focusing with the column and setting the head height exactly between the high and low spot without touching the lens stage 'focus' knob. (exactly like focusing the rear-standard of a view camera). Just stopping down to f16 or f11 and focusing on the high spot (center) won't work.
I really like my glass negative holders, and I haven't had nearly the problems you describe. As noted above, the light source may make the problem worse. I use dichro heads, which are diffusion sources. I also accept the fact that I have to clear the glass frequently. (I use Windex and paper towels.) You also may just be in a dusty place. There are things you can do to reduce the dust. Sealing cracks, plastic sheeting in the right places, dust trapping mats at the entrance, lower traffic, etc. come to mind.
I used to print glassless and started using a universal double glass carrier in my Kaiser enlarger for two reasons. Sheer frustration at negatives popping during exposures and also it is the easiest way to print full frame without filing out a 35mm carrier.