Notice/Vacation Overlap

Would it be a concern to take a less than 2 week notice period (as my new job 'prefers' that I would start before EOM)?

Generally speaking, giving less that the agreed Notice Period is not a good/professional thing to do, as it will give your current company less time to prepare for your leaving.

Personally, I find the timing (vacations and give your notice right away) not the best timing/order possible, but I won't delve into that.

My suggestion and perhaps your best bet is to contact your new/future company and tell them "I have a 2 week notice period to deliver, so it is not feasible for me to start on X date that you mention", and work on a solution together.

Any reasonable employer should understand that and respect your 2 week notice. Some other option I have heard and read of is that your future company 'compensates' your current one for the notice period you will not be serving, in the case they really need you by X date.

As a side note, it's better to have written offer or even better a contract, signed by both parts, and not 'just' a verbal offer; imagine that you hand your notice and the offer is withdrawn.

Go ahead and take your vacation. You work in a state with at-will employment, which means your company legally doesn't owe you any notice at all if it was decided that you needed to be laid off. Accordingly, you don't owe them anything either. Apparently the situation isn't meeting your needs, or you wouldn't be leaving in the first place. This makes anything that you choose to do after giving your notice more of a courtesy than a duty.

HR is already working hiring your replacement. Don't get caught up in sentiment. From their side "business is business"... and you might wanna take the same approach.

Also -- someone pointed this out in the comments. Do not give notice based on a verbal offer. Wait until you have a written offer in your hands!