Hip roof extension

Hi all

I am an owner builder in Sydney with a 1920s brick and terracotta tile home built with an 'L' shape footprint with a hip roof on each part of the 'L'.
I want to add a room inside the 'L' so that the footprint becomes almost square. However I cannot see how i could do this with a new hip roof on the extension without getting a land valley (i think that is correct term) on one of adjoining sides.

Only alternative I can see to completely rebuilding half the roof is to put a skillion roof on the extension with a slight incline. Neither is very desirable, either from a financial or an aesthetic point of view.

Does anyone have any ideas or experience of doing such an extension?

Thanks

Steve

I can't see too many other options. Perhaps you could have a gable on the angle and have the ridge line slope towards the front?