Instead of completely adjustable breakpoints, would you consider a user-selectable breakpoint for the nav banner?
For example, I tend to run across the opposite of the issue here. Sites with only a few main navigation menu items which get the mobile nav menu button in tablet mode. There’s plenty of room for them, and it would make navigation easier if they saw the regular nav bar in tablet mode instead of the menu button.
Currently, the nav menu switches to the menu button for tablet and below. If we could choose (Mobile, Tablet, Desktop) as the nav breakpoint, it would help when there are either too few or too many nav elements at one of the breaks. In my case, I would choose “mobile”, in the OP’s (or Steve’s) case, they could choose “desktop” to collapse it at a wider point.
This would be pretty simple for the user to understand.