I will try to concentrate on the usage of 「～～とする」 in your specific example as 「～～とする」 has a few meanings that are vastly different from one another. The meanings vary depending on the context and/or what words come right in front of 「とする」.
It might be of help to remember that all of those meanings have to do with "making a decision of some sort".
In this context,
「Verb in Dictionary Form + と + する」
means "to proceed to perform a new action (by quitting what one is currently doing)".
New action: leaving before the others leave. （先に行く）
Old action: being/staying there.
Thus, the phrase 「行こうとする」 cannot replace 「行くとする」 in this context as only the latter can be used in announcing to others your decision to leave.
So, how do you translate 「行くとする」? Pretty much anything that reflects your understanding of the nuance "proceeding to perform a new action (by quitting what one is currently doing)" would do.
"I think we should get going.", "We really hafta get going.", etc., perhaps?