Haven't used a Midi Thru box myself but I'm certain that this will do what you want - exactly the situation that the Thru box was designed to address.

Can you elaborate on the chord recognition issues?
I have 2 modules (Technics SMAC 1200 and Solton MS40 and both show exactly the same chords that my driving keyboard displays.
Have used Roland EM2000, Technics KN6500 and Technics KN7000 to drive them with no problems.

The only problems I ever had (and still have) were with the Tyros 3 & 4, transmitting harmony chord data when using this feature - the Technics & Roland could filter this out but Yamaha is not as well implememted Midi wise.
Tony