Had exactly the same issue in the cold weather with my 04 Mondeo. I took out the washer bottle, sealed it all up as I could not find a leak. Put it all back together and it pissed water out.
I found that it was not the hose, nor the pump, nor the elbows but there were 2 small extension pieces fitted between the hose and pump. I removed these and clipped it all together and it was perfect. HTH.

Nice job getting the bottles in and out eh lol - especially in the cold!