The Forward is a much beloved card, but the bottom line is, if it doesn't work for you, it doesn't work for you. Only you can make that decision. Having to force yourself to find use for it tends to mean it's not doing much for you. Yes, the 5x TYP are nice, but if you don't like TYP, then it's not very useful!
I'm a proponent of "if it has no use for you anymore, close it". While closing very young accounts does tend to look bad on manual review, it can be explained to some degree by simply saying you were evaluating options etc. Now, doing it over and over for 10 years will clearly show that you are not being truthful. But none of us are credit analysts and quite honestly, it's not worth fretting too much over the implications of closing an account because who's to say that a future lender will even care? It tends to be a waste of time to worry about things that we have no firm answer about. I'd just move on from the cards you no longer want; unless your util will be adversely impacted, you will not see much score difference if anything.
The only caveat is obviously to mull the Forward decision carefully as you cannot reapply in the future since it's no longer available.
IMO, for an "average" spender, 13 cards is overkill and you won't see meaningful rewards on each one by spreading yourself so thin. Better to concentrate spend on a small handful of cards or less.
