Pittsandpieces, our situations are kind of similar. I'll post it here in case my thinking is wildly inaccurate.
For what it's worth, we reentered on the E-3 after submitting our DS-260 without any issues. It's kind of weird, that you can come back in with a DS-260 in the system at all. It made me kind of worried too, so I searched high and low here and everywhere else on the internet trying to find evidence of a denial due to having submitted the DS-260, and couldn't find anything. The officer just stamped us through and said see you later. One of my other friends who has won as well has been in and out MANY times after filing the DS-260.
Also my job requires international travel semi regularly, I have been avoiding it do to AOS but my friends go in and out all the time, and every time the stamp date and the date on the i-94 changes. One asked a CBP agent what the seemingly random date meant, and he was told that that is when he needs to exit the USA by, when his nonimmigrant status expires. That date is the discretion of the CBP officer every time. For them it is always later than the expiration of the visa, but on our run through, our i-94 date become our visa expiration date, and I'm not sure if that is due to the DS-260 or not.
From what I can tell, we can't enter the USA after the printed date on the visa expires, but we are under that visa status until the date on your i-94. You can read here for more info:
https://www.cbp.gov/sites/default/files/documents/502386 - I-94 Fact Sheet_OFO.pdf
One of my friends has more than a year beyond his visa expiration date on his i-94. You may well find that after this trip your i-94 is extended well beyond your visa expiry date, which should mean that you are good to keep working based off the E3, as long as you don't leave the country. I'm not sure if our DS-260 prompted our i-94 date to match up or not, so your mileage may vary.
If you process with CP, then you will need to fly home for the interview. Looking in the OC selectees thread, most people seem to get their passports back pretty quickly, much akin to an E3 renewal. You still risk having a prolonged processing time, and not being able to return to the USA during that time though.