Well, maybe try my method.

Use Lee push thru dies.

Tumble lube with Lee Liquid Alox, TWICE, letting it dry fully first. If need be, chill the bullets for the second tumble. Takes no time at all to do.

Then with the gloppy lube run them thru the sizer die.

Voila! Lube grooves may not be 100% filled but it seems not to matter. If you want, lube them a third time and when loading, simply pick up the bullet and smear off the lube on the bullet base by wiping on a cloth next to the press. I've shot various bullets at 1500-2000 fps with good results using this method.

Most of the time you don't even need to lube them more than once. I use regular bullets, too, not the Lee Tumble Lube bullets.

If you want, you can hand lube with White Lithium Grease after lubing with Lee Liquid Alox, but the multiple lubing and WLG really is a last resort, the Lee Liquid stuff works surprisingly well once over.