Our group has worked with the local cycling advocacy organisation, including having members sometimes attend their monthly meetings. The organisation has a very good working relationship with the city planning department, and tends to be a strong voice for cycling. We tend to support and publicise each others' events, and work with them on common advocacy issues.
That said, they definitely do not have social justice as an explicit goal, and I have heard of some meetings being heavily dominated by MAMILs, and this is a general issue within the cycling advocacy world:
So I guess the only "if I'd known" advice I can offer is to actively work against by instituting policies that ensure marginalised voices get heard (safer spaces, keeping stack in meetings, etc), and get advocacy organisations who represent marginalised folks involved (e.g., per that second link above, asking BLM advocates before embarking on a campaign to push for heavier policing of traffic offences is probably a good idea).
I guess I should also type up my notes from the Bike!Bike! workshop on combating the white saviour complex. There was some pretty great advice and experience shared there.
And good luck! That sounds like an awesome initiative.
