Panel Set - Make Panel Width the balance of the width?

Is there a way to have a panel set with a defined width panel (300px) and another panel that will cover the balance of the panel set width?

or better yet, a way to set a maximum width on an item that is set to a percent width?

You should play around with the properties of the panelset property “Panel Set Type” 

The fluid with sidebars type does exactly what you asked at first - enables a specified width first column, and the flexes the remaining column to fit the rest of the space. 
The Custom width type lets you specify percentage or pixel width.

Note.  It is tough to actually get to an individual panel’s properties.   You have to click immediately above the topmost component in the panel - inside the grey dotted line that connotes the panel.  Then you will see the Panel Width property. 

Hope that helps you out.