Its an interesting issues as having a EV gives access to the cheapest overnight power
Although, if car is at home during the day, and does a reasonable mileage (bit of an oxymoron, unless you work nights! or have two cars - one-in-the-wash, so to speak) then spilling excess PV to car, instead of using Off Peak (for around 8 months of the year) can help the maths.
Due to roof orientation, shading etc
The shading bothers me, because that can have a big impact. Cut the trees down? (I suppose if that is "
demolish the house next door" that's a bit more tricky!)
Orientation would bother me less. East West (IMO) is far better than South. Twice the roof area to put panels on, and East starts up in the morning maybe an hour before South, and West finishes an hour later - both at times when you are more likely to be at home, and can use the generated power. Whereas if you are out-to-work then the bigger spike, on South, at midday might just wind up as Export. If you have a battery you can shove the South-spike into that, but East /West still preferable IMO. In the morning battery may be border-line for empty, and the earlier sun from East will power the house and in the evening the West will keep the house running later, meaning battery takes over later, and has fewer overnight-hours to support the house (than South-only)
Two roof panels is 2x the number of PV panels, of course, but nothing like 2x the total cost.
Even doing North is worthwhile (provided that the North roof is not too steeply sloping). In Summer North will give you around 75% of South, but because, in mid Summer, the sun rises a long way North-of-East, and sets North-of-West, the North PV gets the benefit of Early / Late generation (similar to East & West orientated roof) and lengthen the "solar generating day"
If you've not already found it have a go with
PVWatts - do a simulation for each roof area / orientation / slope. I recommend looking at the generation for each month (rather than just "annual")