getting (or fabricating) a drop section which already has, on either side, the kind of interlocking slip-on connectors do (essentially a double-fold before extrusion to create the slip-on lip)
reduce the ends of the two 10ft runs and slip them into the drop section then mechanically fastened (screws on the front and back)
I cannot go with seamless since one of the two 10ft segments "belongs" to me, while the other one is the neighbour's (who will have to replace her fascia in the coming years and tear the entire thing down again.)
The 10ft runs are pitched 1/2".
Because the joinery is extremely visible (man's height level and right at the entrance) I would prefer methods #3/#4 over #1/#2 because they have the minimal number of seams. However, I have yet to see an off-the-shelf part fitting the bill for #3 -- and #4 is barely mentioned anywhere.