I agree with most of this except rolling with Rizzi for another year only puts you another year behind on rebuilding the team. Rizzi on a one year deal means no players will respect him because they know he's just a glorified interim coach. Plus, he will not be looking at building a long term team but instead looking at the best team he can have for one year. That means a year where a new HC is not building his roster and implementing his system. Whoever it is that gets the job, including Rizzi, needs to get a long term contract and a fair shot to build his roster and his system.
I don't think Rizzi is the answer and I'm pretty certain we can get a better HC, but if it turns out it's not true you have to give Rizzi a chance to succeed with a long term contract and a chance to build his own roster.
Personally, I think worst case scenario for the Saints is Aaron Glenn. He wouldn't be in my top 3 or 4 picks for the HC job, but I also think he could end up being a very good HC and possibly the best considering his leadership skills and the credibility he has as a former NFL player. I only push him down because he's a D-Coordinator and I really want to hire an offensive head coach since it's easier to hire a great DC for long term than a great OC for long term.