You can do that by using RBF if your wallet supports it.

And also rebroadcast it to more nodes with those websites.

You answered your own question. They do something. They propagate the transaction to more nodes for a higher chance of it being included in the next block. The fee and the propagation work hand in hand to the best of my knowledge. Obviously, I use my own node first, the "ccelerators" are just icing on the cake.