Had another look at both diagrams - I'm not sure this is the problem, but it may be a contributor:
As somebody else pointed out, the original wiring uses negative switching while the modified wiring uses the original negative switching to switch the relays, which positive switch the globes. This means the voltages on the various H4 globe pins change from one configuration to the other.
H4 globes have two filaments with one common pin. From memory, viewed from the rear (and rendered in ASCII

) they are:
High beam --> | _ | <-- Common (Low beam in the middle)
In the original configuration, the common pin has 12V supplied, and the other two are alternately switched to ground.
In the modified configuration, the common pin is connected to ground, and the other two are alternately supplied +12V through the relays.
Do you have the pins wired correctly? I can't work out how it would cause the problem you're experiencing, but let's rule out as much as possible.
Cheers,
Scott