Probably, although the latter is dependent upon NH giving the higher allowance for a flight that's economy connecting to business, which may or may not be their policy. (That's UA's policy, but... 🤷‍♂️ )

Here I could go either way. The single leg in business might be enough to lift the whole allowance to 2x70.

OP: Unfortunately, you're probably not going to be able to get meaningful help prior to the day of travel, even if you go to the airport. What WineCountryUA and I have described is their policy, and you'll be asking for an exception -- meaning that even if you get somebody in a good mood when you ask today, when you go back to take the flight, and you get a different check-in agent, you may get a different answer.

My advice would be to prepare to pay an overweight fee if your bags weigh 51-70 lbs, to show up quite a bit early for your flight, and to ask for the bags to be checked through, explaining the situation. Understand that you're asking for a favor, and make sure that you have a backup plan in case they say no. In the current environment, if you find somebody who's willing to listen, the exception you're asking for is perfectly reasonable. However, not every UA employee is the helpful sort. And, depending upon where you're starting, you may be dealing with a contract employee, who may not even know how to go into the record and override the computer. (If they seem willing to help but don't know how, suggest that they try calling the help desk).