E7450 and 3 external monitors

I've got a C-level user who has a Latitude E7450, and E Port Plus docking station, 2 desktop monitors and a large, wall-mounted LCD monitor.  The E7450 has an Intel HD 5500 graphics card.  What he wants:

• Laptop lid closed in the docking station off to the side.
• Left-hand desk monitor as the primary.
• Right-hand monitor as an extended desktop.
• Wall-mounted monitor a clone/duplicate of the primary monitor (he uses it for meetings at his conference table at the other end of his office).

The wall-mount monitor is wired inside the wall to a wall plate with an HDMI connector.  It comes with a 6-ft cable with HDMI on one end (plugs to the wall) and DVI-D on the other.  He also had a short adpater connected to the DVI end with Display Port on the other which he had plugged into his old HP docking station.

The right-hand monitor is connected with VGA and the left-hand with DVI.

No matter what type of adapters or cables I try in various combinations, I am unable to get it to work as he wants.  We replaced his old HP laptop about 3 weeks ago and it worked fine in this scenario. (I didn't think about diagramming how the various cables were connected to his HP docking station.)  The HP used a DMS-59 connector for the left-hand (primary) monitor.

Some research on a Spiceworks forum lead me to think that my problem is both a display resolution issue (I understand that they should be identical, if possible), and a connection problem.  I had my supervisor get me a DVI splitter so I could take one output (FROM the docking station) and send it to 2 DVI sources.  Can't get the laptop to detect the monitors at all.  Tried on a different laptop, same model, and same result.  I was sent a link to a Dell KB article, "How to configure three (3) displays on a Dell Latitude Portable with Intel HD 4x00 Graphics" http://www.dell.com/support/article/us/en/04/SLN115952/en and I see that DVI has it's limitations with both Intel HD 4x00 and 5x00 graphics cards, but it could be done.  I also saw an article about using Display Port 1.2 in a "daisy-chain" to support 3 or more monitors.  (search using "[DisplayPort Quick Guide] Daisy Chaining 2 to 4 Monitors" as the search term).

My question to everyone is this:  what do you recommend, and why?  I need something I can take to my supervisor as "the" answer.