I'm building a new bike using a Deore T6000 front derailleur with Microshift BS-M10 bar end shifters. I'm having trouble getting the derailleur to shift the whole necessary range and am looking for suggestions before I take it into a mechanic. The H limit screw isn't stopping the travel, since I can pull on the cable and have it shift to the large cog. I've read that if I can pull the cable and shift to the larger cog, the cable is too loose, but if I re-tension the cable with either a frame barrel adjuster or by pulling the cable, I may be able to shift to the outer cog, but the shifter cable prevents the derailleur from hitting the L screw and I can't shift back down to the inner cog. I've also checked my derailleur height and angle and it doesn't seem to make a difference. The parts seem like they should be compatible, but now I'm starting to wonder. Any ideas?
With the cable detached, chain on largest sprocket, set the low limit with the absolute minimum clearance from the chain. With the shifter firmly at the lowest setting (max cable payed out) attach the cable and use barrel adjusters to take any slack out so that movement of the shifter results in immediate movement of the derailleur cage. That should make sure the shifter can pull the cage far enough outboard to get over the big ring.
You may need to adjust derailleur alignment so that the tail end of the cage is toed out slightly to get it to kick the chain into the big ring.
I took my bike to a shop and we discovered that the bar end shifter had been mis-assembled, because I let it come apart when I took it out of the box. This caused the shifter to not have enough throw to shift to the outer cog. I would advise anyone buying bar end shifters to be careful when handling them out of the box. Unfortunately, I don't know my part names well enough, but there is at least one washer-like piece that has to be oriented properly, otherwise the shifter won't have the correct throw. I believe a clue that this has happened is if one of the shifters doesn't reach the same height (physically on the bicycle) when they are on the largest chainring/rear cog.