"my Bosch except it would not recognize a small saucepan"

Bosch cooktop instructions (section 4.2) don't specify the minimum pan size for an induction element. Both GE instructions (page 15) and Frigidaire instructions (page 7) do. The Frigidaire FPIC3677RF might be a good choice if you like control knobs.

Be sure to measure the size of the gas cooktop's cutout before selecting a replacement induction cooktop unless you are planning to also replace the countertop. You'll probably need to add a 240-volt circuit for the induction cooktop; the circuit for the gas cooktop is probably only 120 volts.

Add Miele to your list. And either take your pan into an appliance dealer, a Miele Experience Center, or get a slightly larger pan. Butter melts fine for me in a 10" frypan. A silicone spatula removes all of it.

My Bosch 800 is 5 years old and my butter pot is 4.5” bottom diameter. Works fine. And yes, get RID of your monstrosity.

Why not use a microwave?

I use the microwave for butter but I have a very small frypan for one egg and it works fine on my new Bosch Benchmark.

Putting it inside another pan is a brilliant idea.

My husband used to use his single cup stove top coffee maker on our Bosch 800 cooktop - no problems. It was probably 3.5 inches.

Thanks to all for your comments. Will be going back to the Bosch and using the frying pan idea for my brown butter