Good evening Simon,

You might find a lighter pick gauge will flop right out of your hand when strumming chords faster, especially if you're used to something heavier. 

With regards to avoiding the  Bass E, I recommend you pick one string at a time, individually, using alternate picking (up and downstrokes.) Downstrokes for every string towards the Treble E and upstrokes for every string back towards the Bass E. Practice alternate picking when holding down any chord (technique called arpeggiation covered by Anders in GF2, chapter 1.)

Or you can practice with open strings this if your fretting hand is getting stiff or tired. I practiced arpeggiation like mad at the very beginning of my guitar journey and it really pays off. Especially for focusing on picking strings without looking. This may seem tedious, but learning an instrument can initally be very taxing. So hang in there and don't hesitate to write back with more questions!

All the best,

Drake.