From what I've heard, is its tough to fight an assessment when it is sponsored by the financial company with which you are currently utilizing for your loan origination. Many have "approved vendors". Additionally, its just not likely going to be accepted if you seek to bring in a third party, with a more favorable assessment, and ask the lender to replace their approved vendor. Even though many of us might be honest in our reasoning, the logic behind them disallowing these types of things makes sense. I know plenty of people who were getting crazy assessments ahead of home equity loans during to boom days... it was a scam. Pay the assessor $100 and pick your homes value.
Which brings me to the only piece of advice I can probably give you...let it settle, and then do some due diligence(maybe have your interns do it lol) and find someone who can give you a decent appraisal and then look for a HELOC with a third party lender.
You are in the city so I'd imagine your RE is a reasonably high % of your net worth/capital as you're young and shits expensive there. While I'm in the sticks as you city people call it, I made what I'd call a mistake of doing the same. I bought my home, which didn't kill me. But then followed up with some investment properties as well. All with large money down. And then I started looking at things and realizing that while I appreciated the magic inherent in a 30 year fixed, that I could reasonably expect to do better having much of this cash at my disposal. I looked at many of my options but quickly found out that any kind of RE based financial transaction will likely be expensive. Even my refi, which saved me 75 basis points, added about $8K to my principal balance. After exploring many different things, I just decided paying 3% at IB was my best option if I needed extra cash.
EDIT: If its that low, maybe look to appeal your taxes as well. Then 6-12 months later get a real appraisal and take out a line of credit. Bang em on both ends..
