There are two kinds of "Productive".
There's my personal productivity, and there's the team/company productivity.
When working on a team, you have to figure out what produces the best output for the team as a whole, not yourself.
I function best when I get up at about 8am in the morning, and get to work at about 10am.
Doing that, when others leave in the evening I get several hours of high productivity.
My personal productivity soars when following this.
However, it means I'm much less available for the team, and depending on the project my being available has more impact on the team output than my direct personal productivity.
If you can't convince your manager that it's in their interest for you to have a custom schedule just stick to the mandatory schedule and call it a day. If they don't care about your productivity certainly you shouldn't care either (that's obviously different if you're self employed)
Tech workers are the new factory workers, don't make it more complex than it already is, do your job, go home, enjoy life.