Were Japan and the United States able to reach a compromise and work to negotiate new terms between the two countries?

Yes, they signed Treaty of Kanagawa  to promote peace, commerce, business and safety and security

Explanation:

Yes, Both the countries signed the Treaty of Kanagawa on March 31, 1854 with an objective of opening Japan and its old age policy forbidding commerce with foreign nation. This led to a kind of agreement between the two countries.

The major role was played by the US government that was determined enough to end Japan's self-imposed isolation policy to a close.

The three central objectives were as follows -

a) Provide America's access to strategic energy resources

b) Open Japan's economy for trade

c) Establishing a commercial treaty