I see you are using the networking method of appealing the assessment or getting a work around.
These informal solutions are good as adjunct activity. I do not know how successful they are when done alone. This is because the state property tax laws govern certain aspects of the assessment to which the city must adhere.
My recommendation is to make a formal appeal, by asking for an assessors hearing. You can appeal the assessment based on all the factors, which may result in some reduction. (not just the road)
Constitutionally, your opposition to the road, does not bear merit, for purposes of excluding you from the assessment based on the road itself. That is a issue that affects the common good. You would have to find defect in the process of how they got the road put in, or defect in the valuation of the road and its affect on the property values.
the part you say about contacting board member for a new assessment is on the right track, but you need to make if formal, by letter, and you may want to retain an attorney to help you.
You can also ask for, in a formal letter to the assessor and to the mayor, and the board, a tax deferment.
When you do things informally, there is no compelling legal reason for them to get back to you; that is why you need to make it formal.
the other thing you can do is attend the next city council or board meeting, and make your own proposition to defer the tax to a future year. this way you get the city council to formally make a ruling on it.