So....that was a read.
Let me offer some practical fitment techniques, as none of what we are seeing here is an actual measurement. My experience is with real tooling, which had to have 0.001" precision over a 60" set of dies...so it is less about hand lapping and more about real practical dimensions.
First off, Prussian blue is great. Bluing is much easier to obtain if you're looking for a laundry solution. Yes, you read that right. Laundry bluing. Mix it up thin, coat the metal surface, and let it dry. It's quick, but forms a pretty durable coating.
Now, take your lapping stone. Get one that is larger than the surface you want to lap. Do not use lapping paper or the like, because your inefficiency will screw this up. You are not good enough....because it'll take years of experience to do this by hand.
Now, lap the surface. The laundry bluing scrape off real quick...so only do a few swirls before checking. The lapping disc will become fouled, but a quick shot of water will clean it up.
Continue lapping until the bluing just barely vanishes, allowing the lapping stone's weight to keep it centered on the surface being lapped. This takes time because you aren't applying a huge force, but be patient. If you've thinned the bluing enough the resulting surface is going to be flatter than you'd image, and depending upon your lapping stone more than flat enough to meet requirements. I used this stone on tooling steel...your mileage may vary, but a silicon carbide may be better:
MSC - Lapping Stone
Once the CPU is lapped, you need the same finish on your block. It may be non-ferrous....so do be warned that aluminum oxide stones here are a huge issue. Use the right tool. Coat the lapped surface in laundry bluing, cut with a little bit of liquid detergent. This sounds silly, but you'll need time. Install the CPU and the block, with the lapped CPU getting a skin coat of that bluing mixture. Give about 2-3 hours to dry, as the laundry detergent will become tacky over time. Once there's a crust on the edges of the interface, pop it loose. The lapped CPU shouldn't retain much if any of the bluing/detergent mixture but it will stick to the block.
Repeat the lapping technique from above, tilting the lapping block slightly to make sure any thick areas of the resulting bluing mix are lapped more aggressively. This will not give you a perfect interface (we had to lap on a flat table to get a true interface), but it should get your lapped surfaces aligned and correctly lapped enough to make much better contact than when you started.
Now, to the thermal loading shenanigans. Let me suggest that dies used in metal expanders don't consider thermal expansion. That is to say that the dies are installed with a cool machine, then during running they shear and stretch sheet metal inside what is basically a very large set of scissors. This generates a temperature very near boiling....which is a delta near where CPUs operate. If you install a die set there with a 0.001" spacing between blades it's still a 0.001" spacing under full loading, because you're looking at internal forces evening out the thermal load. Believe it or not, they're not huge. Because you're already taking up the slop of stresses with your block installation kit, it's unlikely that thermal cycling will ever apply enough stress to damage anything. I watched people install a blade and die set pressing the blades to dies (a functional 0.000" clearance), and the failure mode was material feed and not blade damage. Yes, you can have scissors/shears too close together to cut material.
