The car park at the ground is fully used up by season ticket holders so just dump it on a street nearby, it's what we did at York Street where things were arguably even more packed. I wouldn't worry about irate local residents either, just don't block a driveway or a pavement and you're well within your rights to park where you want.
Shuttle bus is decent enough if you're willing to stump up for parking in town on top of the bus, takes about 8-10 minutes from town, but the times I've used it it's hardly been used so no idea how long it'll last as a service.
ALSO - I know at some point Costa were letting fans park in their car park right next to the ground for £5, not sure if that's still a thing though, anyone else know?