I-30 to 635 west to 114 West
I'd probably go this route, you're most assuredly going to encounter some heavy traffic regardless of the route coming in from the east
You're right Westside, really no way to avoid heavy traffic trying to get to Justin from the East. I had enough of it years ago, figured out I exit off of 80 at Sunnyvale, Collins Rd and cut up to BobTown road, then to George Bush Turnpike, to 35E, a few miles north on 35E, then 407 through Flower Mound all the way to Justin.
OP, you do have the option of exiting 30 once you cross the Ray Hubbard bridge, near Bass Pro Shops and getting on George Bush Turnpike and following it around all the way to 114. It's longer, but may be less traffic for you.
Edit: Or.. avoid 99% of all that metro mess and take 380 from Greenville to Denton, then 35W south down to 114.