I hadn’t checked this forum for a little while. Glad to see there are new visitors!
Atembedded – Check out the post at http://www.singleservecoffeeforums.com/dissassembly-repair-guide-keurig-b70-platinum-t8124-150.html#p92769
, or just go to the end of page 10 and read Black Rose’s post, then on to the first few posts on page 11. EmmJayEff discusses the issue there. The bottom line is that you might consider that instead of having priming problem, the check valve that is in the line between the water pump and the hot water tank might be getting stuck closed and preventing water from filling the hot water tank inside. I also remember my B66 behaving that way, and I had to keep removing the outside reservoir and reseat it to get it to fill the inside tank again. What I remember doing to fix it was to clean out this check valve. I already had the unit apart, so I removed the water pump and disconnected it from the tube that leads to this check valve. I then took a long cleaning Q-tip and inserted it into this line and used it to clean the tiny bit of buildup out of the check valve (I think it came out vaguely green). If you have the bottom off of the unit you should be able to do this without disassembling the rest of the whole unit, since that would be a lot more involved than just removing the bottom. Of course, before doing any of this you should de-scale the unit with white vinegar, if you haven’t done that already. That process might remove the buildup in the check valve without going to the trouble of taking it apart.
Another thing I might mention is that I discovered that the plastic screen that is inside the external reservoir inlet seal is actually removable and cleanable, should there happen to be debris in it. I discovered this when I accidentally knocked it out of position. You can grab it by the + (cross shape in the middle) using a needlenose pliers and gently rock it out of position, then remove it and clean it. When reinserting it, it does need to be lined up exactly the way it was before, so make a note of how it was pointing.
As for the extra tube at the pump inlet that lets air in - since it is connected to the input side of the water pump, there should be suction present there, so I believe it’s purpose is to simply vacuum water out of the places where it shouldn’t be – like the aft solenoid valve and the air pump!
DM in AZ - For whatever reason, when I took my B66 and B70 apart, I didn’t want to drill into them to disassemble them. I used a very long, thin, regular bladed screwdriver to get to at least one of the top cover latches that were accessible through the bottom. However, I could push as hard as I could on the latch, but couldn’t disengage it. So instead I placed the corner of the machine that had that latch firmly on the workbench to brace it, lined up the screwdriver as before, and tapped the screwdriver handle moderately hard. With that, the latch actually released fairly easily (I had to pull on the cover at the same time to get it to separate though). After getting that first one loose, I was able to create enough gap in the cover that I could get the same screwdriver in through the gap, to access the rest of the latches and release them by tapping the screwdriver handle the same way. So for me, hammering did the trick – easier than pushing. Once inside, I also beveled the hooks to about a 45 degree angle like you did, because I didn’t want to go through all that again.