Can anyone help please?

My garden Shed roof is leaking due to sagging. The roof is 11 foot 6 x 7
foot 6 with a 6 inch drop.
The shed was handbuilt (poorly) by the previous owners and is covered in
felt over tongue and groove boarding. The 2 supporting beams are along the
long axis rather than the shorter one.
Each "beam" is are made out if 2 lengths of 1 1/2" x 1 1/2" with a short
length of the same bracing them at the join (something like -_- ).
This has caused the centre of the roof to sag and leak. I have tried bracing
the roof with poles and sealing the joins of the felt with bitumen paint
with limited success.
Can anyone suggest a good to fix this? I am reluctant to replace the entire
roof as I'm not that adventurous with DIY and I don't think that the weather
will be kind enough to allow me an extended fixing period.

I was considering fitting a second roof over the first by constructing a
frame (with the main supports on the shorter span), boarding and felting
this.
This will hopefully allow me to increase the slope of the roof as well. A 6"
drop over 7 foot 6" seems a bit shallow to me.
Is this a relatively easy job? Or would removing the existing roof and
rebuilding be a better bet?

All suggestions gratefully received.