Have you considered using a stationary trainer? Maybe even Zwift? It would allow you to pedal at a constant load for as long as you want. I used one sometimes before I retired.
I know what you mean about trying to put out a steady effort with all the "interruptions". It's one thing I like about long climbs, just finding that rhythm.

If I'm tired from a hard ride sometimes I'll take the mountain bike and just noodle around the neighborhood, go in a creek bed, etc. Then I don't mind the interruptions.