1) Superman Shouldn't Fly.
2) He shouldn't have a cape
3) He should fight a Giant Spider
4) Brainiac should be the villain.
5) Brainaic should have a flamboyantly gay robot sidekick.
6) Brainiac should fight a Polar Bear.
I think that'll satisfy the no tights no flight crowd.
Lets call this new film Superman Unleashed, inspired by The Force Unleashed. The entire point would be to have him use his powers in the coolest ways possible.
First thing, we tone him down a little. No flying FTL, time travel, or moving planets. We can keep it at a reasonable Low Silver Age/High Dark Age without hitting heights of absurdity like altering the very nature of reality by punching it.
And now that we've put some limits on his powers, we set about figuring out how to use them in the most awesome ways possible. To do that, we need a villain who can survive a Superman's best. Doomsday is tempting, but flat. There is nothing interesting to be done with him. So I would suggest Darkseid. He has an army, he has a motivation, he's a complex character, and he's all but invincible.
No origin story, of course. That gets in the way. It starts with Superman kicking butt and doesn't slow down.
On the relationship angle, Supes is more open and and honest with those in his life. Lois knows his identity and is living with him, providing him with emotional support in addition to kicking butt in her own right. She is never captured and is not a damsel in distress. There will be no rescue missions. There wil be no hostages. Superbaby can be ignored or included, depending on the direction they want to go. But he shouldn't be important to the plot. He's a kid and he's strong, but he can't do much against parademons, mostly because he's just a kid who happens to be strong. He doesn't develop any other powers.
Frame the conflict between Darkseid and Supes within a higher moral conflict of control vs freedom, tyranny vs chaos, safety vs risk, and efficiency vs compassion, with Superman seriously questioning how far he should go to save lives and if his unwillingness to step outside of his moral comfort zone makes him just as guilty as the countless criminals that he doesn't stop, precipitated by a disastrous suicide bombing that he could have stopped if he were willing to use lethal force against the bomber. Not angsty, of course. Superman and angst don't mesh, but just trying to feel out the limits of his moral obligations to the people of the world.