We need to know if there is winter where you live to answer this.
If your gutter is high to deal with tropical rains, you may be flooding the basement by cutting notches. If you get Ice damming today, this could be a bigger issue than I realized earlier.
My suggestion is that you keep things clean and watch what happens. If you continue to have issues, then you need to spend money. If not, you need to find a gutter cleaning schedule and procedure that works well for you.
Finally - be careful up there. We lost a neighbour to a ladder accident this past weekend.
North Florida - no real winter, but it does usually get below freezing overnight a few days per year, although I don't think it did this year. No basement. This is also a solid 10 feet from the edge of the actual house, being at the edge of the porch. The water backs up the porch roof, I think all the way
Terrible about your neighbor. Luckily, ours is a single-story house, so relatively low. Still get pretty nervous if I'm on the roof near the edge, as I pretty much have to be to get at one section of the gutters. Falling from 3rd or 4th rung of ladder or a ~10 foot roof is still a recipe for a very bad day, so yeah - everyone stay careful up there!
So voting no to the notches, at least for now?
Just for clarity - the initial question was regarding the front-of-house gutter, and that appears fixed to me after clearing out the clog - was up there with a hose after unclogging the thing and it looks to be flowing pretty well now.
The back of the house is quite different - the screened-in porch covers most of the length of the back of the house, and has this strange geometry. Neighbor says that a prior owner of our house that bought back in the late 80's worked in a metal shop, so a lot of metal appendages to the house like this porch-with-integrated-gutter that look pretty good, but don't strike me as very well engineered upon closer examination.