Functionally impossible. Even if they aren't allowed to own anything, you can't stop people from doing them favors of one sort or another. You'd basically be making it a rule that their reward for their work is getting discreet favors from special interests. It'd be hard to establish a set of rules airtight enough to stop it from happening entirely, companies would find ways around whatever basic regulations are put in place just like they do now.
I’ll be generous and they can keep their current salary. But no additional income streams allowed. And all investments must be held double-blind and only invest in broad index funds.
That’d be a good start. An unforceable but public vow of poverty upon swearing in would still be good.
You went the wrong way. If anything they should take a vow of poverty.
What’s that? Then no one will want to be a Senator? Good.