Here's what I do, I find a card with a great deal (like $400 or $500 for spending $3,000 in 3 months) and I use that card exclusively until I reach the target dollar amount. Once I reach the target dollar amount, I cash out my benefits and move on to the next card, or go back to my go-to daily use cards like Chase Sapphire preferred or Chase Freedom if there aren't any good deals running. If I am buying plane tickets to Thailand or making big purchases, it might take me a month to hit the dollar amount, if I am not making big purchases, it might take me the full 3 months.
If I am taking a trip where I want to use up the free airline credits on my Amex cards, I will bring those cards with me and buy seat upgrades or drinks or movies or whatever just to use those benefits. For the Amex platinum, I might use it on two or three trips before I hit the $200 airline credit limit. Either way, the refunds post before the bill is due, so I pay it as soon as the refunds post, then put the card in the drawer until the next year.
At no point have I ever carried a balance on any card, because I don't want to ever pay a cent of interest. I have also never paid an annual fee, they are either waived for military every year, or I get the first year for free, then drop the card down to the non-annual fee version at the end of the year.
This might all sound like a lot of work, but you can easily manage all of it on your iPhone while taking a dump.