A couple things to consider here.
First, your support is utterly irrelevant to BLM. Let me repeat: they do not care if you support them. After all, moderates such as yourself, S*****, K***, etc. already "recognize the plight of black people in America." What this means is that, regardless of what BLM does, there is a very good chance that you'll support a big chunk of their strategic objectives anyways. You'll support body cams, ending racial profiling, better resources for public defenders, ending all discriminatory sentencing practices, community policing, ending the War on Drugs, better education in ghettos, that kind of thing.
Second, BLM does not exist to convince other people that they are wrong and BLM is right. As S** pointed out, BLM is combative and radical. The reason they exist is to set the outer boundaries of acceptable action and speech in these times, and to keep these issues at the forefront. They could honestly care less if you agree with them. In fact, if you disagree with them, all the better, because that creates opportunities for them to make sure that this debate doesn't slip from the collective consciousness, as it has time and again.
Third, the reason why BLM is so decentralized, and lacks a real leadership structure, is due to the point made above. They aren't trying to lead the charge. They are more like the drummers in a war party than they are the rank and file. Their only job is to intimidate the enemy, provide a focal point for unit organization, and rile up the troops. The people who do the actual fighting - which in this analogy means mundane things like knocking on doors, mailing newsletters, petitioning Congressmen, attending council meetings, etc. - are left to their own devices, to do what they do best.
The effect is is simple and effective: you can either implement reforms requested by 81 year old Dorothy Walker in the council meeting, or you can go back outside to get harassed by the mob. Either way, the issue of race isn't going away. BLM will not compromise and it shouldn't. You can argue that their methods are rude, insensitive, uncaring, irresponsible, whatever. The point as I understand it, is that we are finally seeing another authentic black movement, driven by youth, that wants to address serious issues in their community.
Some people in the movement are stupid, some are mean, some are amazing, most are just average. So what? Are you really going to stand in the way of progress because the methods aren't pure? Of course not. You'd say Obama was a good President, despite the fact that he is responsible for killing thousands of innocent people. And yet BLM, a group with tens of millions of supporters (65% of blacks and 40% of whites in America), should be judged on the actions of two men? It is absurd. BLM deserves your support, even if it doesn't care for it.