Orange Man,
As your steels are up, it is a bit in late in the day now to alter roof. Was going to suggest change roof design falls, and let flat roof water discharge over top left hand side., leave of ridge tiles left hand side, substitute with lead cover flashing apron either straight or scalloped.
Done it a few times in the past, and it does not look bad.
Or all as above but use ridge tiles, but leave one ridge out in the centre and in this section form open hopper chute for water. to run down tiled roof
Or leave half ridge tile out left hand side against existing house, form open end chute and secrect gutter under toof tiles and to fall of roof.
We have done all three in the past and never had a problem..
By now you should have better knowledge of your problems and would suggest a meeting with your Arch and ask for his opinion.
Afraid that we can not be of any further help to you, Hope the sun shines on your progress, and would appreciate seeinag a photo when finishsed.
Regards oldun