I think it's a combination of the first two points you brought up.
How are you holding the pick? Gripping too tight? Don't.
Don't dig in too much.
Don't have too much of the pick tip exposed.
Use a
Dunlop Jazz III pick (sharp point = smoother, faster picking).
Lighten up your touch all round.
Try to pick more from the wrist than the arm -- picking from the arm is an awful habit and looks amateur.
Let the pick "float" or glide across the strings and and avoid pressing your forearm or wrist too tightly against the
guitar body.
Stay relaxed but keep a certain amount of snap and aggression in your picking hand.
Economise movements.
Practice picking on a single note, single string. Get it as fast and smooth as you can with minimum movement.
Experiment with different positions until you're comfortable.
Try using the pick at different angles.
We've talked plenty about modes here in the past . Do a forum search and ye shall find.