How are you calculating your HR zones? Max HR really doesn’t matter. I’d recommend doing a LTHR test to get your Threshold HR and then calculating your zones based on that.
Your HR will likely vary from inside to outside as there are many different discrepancies between the two riding styles/environments, such as temperature/cooling, muscle recruitment, mental engagement, and potentially power as well if you’re not using the same power meter in both scenarios.
This might be a bit of a hot take for some, but I’d recommend going off HR when riding in Z2. Power is great for a lot of things, but when you’re looking to keep your metabolic state in a specific place, HR can at times be more accurate as it shows internal strain rather than just energy expenditure.
There are, of course, things that will make your HR less useful, such as if you’ve consumed caffeine, illness, excessive fatigue, etc., but for the majority of my training purposes, HR works well for Z2.