Never mind omitting slogans, what if the differentiator is a lack of any such overt messages at all? Bear with me on this, and it's probably total naive shit...
You take existing local issues - filter out the lost cats and here is a good example:
SalfordOnline - plenty of unaffiliated small-p politics on there, people with housing issues, commentary on local planning, etcetera. Taking this and similar as the feed, you develop something, I don't want to try to name or describe it yet, that provides support to people whose only other route is the failing establishment.
The causes you pick are based on little more than need, and the support it provides is whatever practical aid you can provide - mentoring, direction, legal knowledge, pressure on authority, how to run a good campaign, pro bono professional inputs, etc, exactly the sorts of thing that we would do well at if someone asked for help on here.
From this inherently flows the things you are talking about, without ever being called out and without an explicit ideological basis. You haven't had to read chapter & verse to anyone on class struggle or solidarity because it's part and parcel of what you're doing - you're never being asked to do anything contrary to these things. You haven't had to set up monolithic campaigns or meetings in the first instance because you're doing direct legwork. The only fundamental aim is to make it snowball and solidify into something cooperative that can find or attract people in need, and can attract more loosely political people who can help that would otherwise have trouble finding anywhere to direct their efforts.
It's full of challenges - building the initial network, hijacking, egos, lack of focus, not remaining forever piecemeal, ending up being top-down Momentum etc - but it attempts to avoid a highly partisan and dogmatic core that often destroys itself before doing anything. You can't be blamed for the historic failings of whatever affiliation it would have normally had, because nominally there isn't one - can't slag people off for just helping each other. The risk of it being subverted is much lower than the risk of it achieving nothing, and in its worst outcome it probably still helps a few individuals, like a shit version of Helpfulpeeps. In a way it is a covert, unlabelled version of whatever you might have tried to achieve anyway.
Something to dissect anyway?