I think you just need to save up enough cash to be able to cover a $5,000 bill. I would keep putting it on your own card if possible, get a 2% back card like the Citi Double Cash and you make a $100 profit each time you pay for one of those $5,000 dinners.
Also, if you are paying the balance before the statement hits, it will not be counting as 50%+ utilization.