I think you are probably underestimating the stress levels this will put on you and the family.
As you know, on days like today, getting in and out of Newark when there are storms in the area could be a nightmare. Because you have a meeting on Mondays you want to be there for, I think leaving at 10 to be at the meeting is cutting it pretty close.
I also think getting to Newark without traffic is a very wishful dream on your part. If it's not traffic, it's construction. If it's not construction, it's an accident.
I think you may want to consider either an earlier flight on Monday or even the last flight on Sunday evening.
It however is a great offer, the ability to have the commuting expenses picked up so you can make sure it all works out for you.
Hows the rest of the family with it? There's probably going to be some stress those days without you around, don't dismiss that either in the equation.
Welcome to flyertalk, it's going to be a tough decision either way, I think the plusses and minus points on moving and staying make either decision about the same.
Though, of course, if you move you won't get those 1,400 or however many miles it is a week.