Bike fit / correct riding position

I have an Orbea Onix much like this...

I'm 5'9", the saddle is at a reasonable height, I have recently lowered it even, 90mm stem. But I find I have two problems;

1. If I sit properly on the saddle I feel as though I am pushing forward on the pedals, so I sit on the front of the saddle to bring myself over the pedals, but I also feel a bit stretched to reach the bars.
   
2. When honking I feel like I am too far over the handlebars.
   
   

My theory is that I need a frame with a steeper seat tube angle, this would bring me closer to the bars and bring the BB further back under me, and with the BB further back I won't feel like I'm on top of the bars when honking.

Any other ideas?
Anyone know where I can go for frame fitting in Liverpool?
Any recommendations for road frames with steep set tubes?