I am working on my 3rd battery. The second was replaced by Microsoft even though it was just out of warrantee. Thank you.
Some observations
The screen shattered when I tried to disassemble. One really needs to heat it to 100c to allow the glue to melt. I did not invest in "heating kit" but I did buy a tool set and tried a hair dryer. In any event it took several weeks working part time to scrape all the bits and pieces of the old screen and remove the battery. I managed to locate most (but not all) of the screws that hold the motherboard onto the case and lifted the board enough to remove the battery wiring. I also noticed that some of the screw heads were stripped as the repair center had as much trouble removing screws as I did. Some screws I had to use needle nose plyers to turn as the Torx simply spun on the screw head. Only a few screws were damaged and none by me.
The new screen I got on eBay flickered as it was a Samsung made in 2015 and I returned it. I got an LG surface pro 5 screen and ribbon cable adapter to surface pro 4. The new screen worked perfectly. I did not glue the new battery in and will use only a few "cut" pieces of the adhesive tape as I do not want to go through scrapping all the glue out again for the 4th battery.
I had one screw left over after re-assembling. There was a hole for it but the screw was not long enough to tighten and I do not want to take it apart to find the correct screw.
I will never buy another tablet, netbook, or laptop without checking the "repairability index" first.