Why not make it audible?
That means the pitch drops to nothing as you approach 1:1 VSWR.
Here is a simple 555-based voltage controlled audio oscillator (designed by Drew Diamond VK3XU) that can be connected across the meter movement of a VSWR or resistance antenna bridge. The meter still works but you get a tone as well.
Watch the video to find out more.
Want a self-contained unit without the meter movement? Here you go.
There's other applications for this as well. For instance you could try it in a Wheatstone bridge circuit to measure resistance, capacitance or inductance. Or any other application where you are adjusting a meter for a null. You might even be able to save money by removing the meter movement altogether and just rely on the tone.