Is the lap substrate a ground surface?
Does it have a convex curve that matches the mirror?
The lumpiness is not so unusual.
It happens sometimes with a new lap, and after a little work to break the lap in goes away. Probable reason being the new lap has not yet been completely pressed to full contact and polishing agent not yet uniformly embedded in the pitch surface. Just my opinion, don't know for sure.
I have seen this occur when working 8 rotation positions of the mirror and or lap. I Don't think you are doing that.
Another cause is excessively wide channels, and this is probably the major contributor in this case.
I have never needed to use mineral spirits or turpentine to get pitch to stick to a glass tool, but I don't cast the individual squares, I pour the lap either on the tool, or on the mirror and set the tool on top of the pitch.
After making and wrapping a collar around the mirror I rub a few drops of vegetable oil over all the mirror surface, place a piece of aluminum foil on the mirror and rub it into contact with the mirror and rub the wrinkles out. Neatly fold foil up an the collar to make a dish to pour the pitch into.
The collar is made to precise width to extend above the mirror surface the desired thickness of the lap. I like to use strips accurately cut to width from paper poster board to make the collar because it's strong enough to hold up to pressures likely to occur when placing the tool on top of the pitch.
Width of the strip is substrate thickness + desired lap thickness.
With collar taped tightly in position around the mirror, level before pouring.
Melt enough pitch to fill to the top of the collar.
Pour pitch to top of collar.
Carefully place tool on top of the pitch, making contact with the center of tool at the center of the pitch. Carefully lower the tool until the the edge of the mirror is even all the way around with the top edge of the collar. Don't press the mirror past the collar. When the edge of the mirror is at the collar all the way around there will not be much room for the pitch to come out at the edge. A little, very little might come out before getting the mirror edge all the way to the collar because the tool is convex and extends past the level of the collar, very little for a 6" f/8.
I recommend thickness between 3/8" and 1/2", let's say 7/16" thick. This is so you have enough thickness so the lap will last long enough to make a few mistakes on the way to the parabola, or maybe your finished lap is thinner than planned. Some people like 'em but at abut 1/4" thickness the lap is very close to being to thin for me.
Another method I've used similar collar on the tool (no oil or foil). Pour thick slow pouring pitch on the center of the tool, cooling pitch piles up and domes in the center. Mirror face coated with thick slurry is pressed down on the dome, contacting center of mirror to center of pitch dome. Pressing mirror down spreads contact across the mirror face center to the edge.
Need to pour the right amount of pitch so the dome fills the collar when the mirror's edge gets to the collar.
If you want to try one of these methods let me know, I can give some more detail.
Both of these form a curved surface on the pitch and will quickly press to full contact.
I cut channels with a single edge razor blade.