Welcome to the forum
TBH I can't think of a way other than you are doing, but it might help to use a deck scrubber. I found I quickly wore the bristles out on mine, but the wooden head is held on with four screws and I replaced it with an actual scrubbing brush, which was a lot cheaper and had the advantage of a pointed end. I use bleach on mine and wash it off onto the lawn, which doesn't seem to mind, but it must be fairly dilute by then. I look forward to seeing if someone comes up with something better, there is a wealth of knowledge out there in this community.