You've done a good job with the analysis. The other factor that you need to take into account is time. How long do you see yourself at the other place? If it's 2+ years, then this sounds like a good financial move. If no more than one year, then the math is pretty straight forward.
U-haul is typically a no more than a couple hundred at most (likely less).
I don't know what your wages lost will be. At $20/hour that's about $160 for an 8 hour day, but take out your taxes and that's less than $150. (These last two I'll just tag at $200 each for simplicity. That's likely high in total but will account for some of your 'extras' you'll end up buying at the new place.)
So total up front one-time reductions in money are $1,400 + 200 + 200 = $1,800. I don't consider the $1,200 something to take into account from a savings standpoint. It's a deposit and something that has to be paid, but you've already accounted for the fact you're losing $1,400 at your existing place. So.....
1 year: 2,400 - 1,800 = $600 saving
2 years: 4,800 - 1,800 = $3,000 saving
3 year = $5,400, 5 year = $10,200
For me, if I liked the other place and planned on being there longer than a year, then this is a no brainer to move, and if you're planning on renting for a long time, this is extremely attractive.
Note: Before you make a decision, make sure you are 100% certain what you'll be paying if you break your current lease. State laws vary but most say you are on the hook until the end of your lease or until the landlord finds someone to take over the place (whichever is first). Your lease typically is allowed to lay out something different which might be what you've already researched and know.