The answers to many of your questions are in CFR 1.408-11:
https://www.law.cornell.edu/cfr/text/26/1.408-11
"Would the Adjusted Opening Balance be the exact balance of the accounts the very day before the contribution was made?"
It would be the account value immediately prior to depositing the $6,000 contribution.
"Would the Adjusted Closing Balance be the exact balance of the accounts the very day we remove the contribution?"
It would be the account value immediately prior the the distribution of the return of contribution.
"Would we have to ask Merrill Edge and Fidelity to provide us with the exact account balances for the Adjusted Opening Balance?"
Yes. Merrill Edge and Fidelity should do the calculation for you, but you should obtain the relevant account balances so that you can perform the calculations yourself to verify what Merrill Edge and Fidelity calculate.
"Since we're 35 we'd also be charged a 10% early withdrawal penalty, correct?"
Only on the taxable earnings.
Regarding which option to pursue (return of contribution, recharacterization or keeping the excess and applying it as a 2022 contribution) depends on a number of factors. Recharacterization allows you to keep a contribution for 2021 but will be nondeductible if either of you is covered by a workplace retirement plan. Keeping the excess contribution, paying the 6% and resolving the excess in 2022 with either a regular distribution after October 15, 2022 or using the excess as part of your 2022 contribution depends on how much investment gains you have as you approach the October 15 deadline to do a recharacterization or return of contribution and how much you'll end up being eligible to contribute for 2022. I usually use a 30% gain as the threshold for keeping the excess in and resolving the following year, but that's just a rule of thumb.
