John,

I installed the same type gauges in the same place on my LNC2 and had no trouble with bleeding the system.  I tried to fill the vertical lines before screwing on the gauges but that was really messy and hard to tell how much really got in there.

It seems to me that if there was a little air in that portion only (namely above the horizontal lines on the floor in the photo) that this would just act like an accumulator to hold pressure longer.

I think this whole process is quite different from bleeding our toe brakes.  In the gear case, the pump runs till it gets the needed pressure feedback unless fluid is flowing past seals where it should not.  The pump doesn't care if there are a few air bubbles somewhere in between as long as the pumping element is completely wet with fluid and not air.  With the brakes though, ANY air means the master cylinder piston moves farther than it should and we run out of ankle leverage.  You can't just push farther and get the pressure up.

Because of the above, and assuming you do not have visible external leaks, It might be prudent to get a bunch of AN plugs and isolate all the cylinders and the dump valve as you described.  Then pressurize in one direction to see what you get.  If it pumps up OK, then try the other direction.

If that all checks out, then re-insert the dump valve and try again.  This should show that either the dump valve or at least one cylinder has an internal leak.  Now, with a known good dump valve, re-connect the gear cylinders one at a time with an up/down test of each one separately.  Connect up the gear cylinder with the longest run first and work back toward the pump.  You could connect the corresponding door cylinder once that gear cylinder is proven to work.

This looks like a new airplane, so maybe all the o-rings are just too old.

Good luck

Tom