I don't think we should use the same strategy that Cleveland is using. It'd hurt the fan base a ton and would take probably 3-5 years.
First off - you have to sacrifice $$$. I don't think an owner who just dropped 1.4 bil is looking at running a profitless NFL franchise. They're eating 35 mil in dead cap in 2016. They play in an empty stadium. Odds on favorite for worst merch in football. You think the owner there is making like... any money outside of what he's guaranteed from the rest of the league, and away games? Probably not. He might save some money on marketing, since there's no point of having a marketing team since everyone knows you're polishing a turd. They do have the benefit of paying their team the least to the cap even with the penalty. So its pretty obvious why they're so bad...
2nd - you're sacrificing time. They're at least another year away from competing, they don't have a qb, they're absent any playmakers on offense really (Pryor i guess but hes UFA anyway. With their cap rollover for this year they have 100 million in cap space - and will have a hard time spending anywhere near that because no one wants to play for them. They can front load a contract or two, and probably pry an RFA or two away without draft compensation. But this will again cost the owner money because of all the reasons above.
Now what they have done that's great
Traded busts for pennies on the dollars, or cut them. All this did was push all their cap hits into this year/next year (this year was lost anyway). They got rid of gilbert, mingo, manziel, Kruger, bowe, and whitner. They basically said - the old regime sucked and wasted money so we're starting over. They didn't try and market or sell tickets for this season.
That was smart from a building an NFL team perspective, but it also builds apathy in fans.
Money paid upfront is typically split over several years. If you cut or trade someone prior to the last year that bonus money is paid - then you pay the remainder up front when you cut/trade them. When a teammate "restructures" base salary to bonus money etc. to create cap space this is what he's doing. Ensuring that he get's paid money as a bonus over several years instead of needing to be on the roster to get paid via base salary.