I wonder if you have tried high % menthol alone?

I use Biofreeze for burning pain... 3.5% It also has Ilex in it which is an antioxidant. It always works for me.

The mechanism for menthol is this:

There are two temperature type nerves, one that relays heat and one cold. The cold sensors have neurological priority in reporting pain. (I guess this is a survival mechanism).
So when the cold sensors are stimulated by menthol, the heat ones never get registered by the brain as long as the menthol is there working.

So it is no surprise that the mixed patch is working better.

Menthol is often added to compounded dermatological creams too, for patients with chronic itching problems. But that dose is much lower in range, more like .25%.

We have had several discussions on the subject of Menthol. You might do a search here to find them.