Yep the CF is great for an original layup but not worth the expense for a patch. Looks like you have chamferd the area well enough though it's hard to tell dimensions from a picture. Stick with the 1708 and poly.
IMHO cutting just the cap of a stringer and digging it out then fitting a new one in would be tedious and time consuming, not to mention the bond may be questionable. I would consider taking all but an inch out so you have a bit of a guide.
You need a motor, get one, what ever it is the folks here know how to install it. You get a motor and help is available. Lots of opinions and most are good.
Yep, some times folks have fun but not necessarily is it help, although most of the time the information given will be useful but maybe not for the present question.