Yes, it does look odd.

Perhaps it should have been: In August, House Democrats to propose ban on lawmaker stock trading.

Yep. Currently reads like they're going to propose... something (marriage?) "in August ban on lawmaker stock trading". Problem is that phrases like "August ban" are common in headlines, but that's not what's intended here—it's not saying "the ban that happened/will-happen in August", as in "alleged mob boss nabbed in August sting operation", but describing when they'll propose a ban.

A fix could indeed involve commas:

House Democrats to propose, in August, ban on lawmaker stock trading

Looks fine to me. If the modifier were placed at the end of the title it would be misplaced and would imply what you've said.

Confused as well. I read it as ban only applies to August and was wondering what was special about August. Think it’s missing at least an “a” before ban but ideally a comma before that too.