Running app that logs 'exercise minutes' to Apple Health?

Hello - I have tried almost every running app in the app store (Nike, Runkeeper, Map My Run, Stava, and many more) and not a single one of them has access to write 'Exercise Minutes' to Apple Health (Looking at the 'Data Sources & Access' section of 'Exercise Minutes' in Apple Health).

My work's benefit program offers discounts, etc for health insurance if we track our exercise minutes in their app (which has 'Read' access to 'Exercise Minutes' in the app).

What am I missing? What apps for running are available that write my minutes I have run to 'Exercise Minutes' in Apple Health or do I need to reach out to maker of the app for my insurance and suggest they try to read the minutes I exercise from another data source in Apple Health?