Slightly different take: cool your jets for a few weeks after move-in. Get the lay of the land, meet the neighbors without any insinuations of audio - get to know any who are willing to know you, as people instead of as assumed hobby obstacles to be convinced / woo’ed - for most people the former will go more naturally which is to say, less awkwardly. Use headphones during this time. I would not ask a neighbor I do not know well to do loudness / listening tests with me. That injects bias for concern in people and requires assuming they’re of similar personality / affability as you. It’s a risk, surely.
If your speakers energize the room for your boundary composition(s) / thickness / etc., no amount of wool or slab or otherwise will help unless you rebuild said boundaries - some room modes may be well away from your listening area and might not be on your side of the floor/wall, again depending on boundary composition / spacing. If it’s all wood and/or drywall, it’ll potentially be a real problem if you have a pair of intolerant ears opposite said boundary(ies).
During that initial “down time”, see what other sonic perturbations come from the building, the area, what times of day, etc. Educate yourself on relevant dB ordinance / statutes for your city / district.
I agree 60’s dB listening is not loud, so it will probably depend on how your bass peaks behave in-(and beyond)-room. I certainly wouldn’t sell a pair of speakers I really like for living a while in that type of place, at least not right away before I had lived in said environment and knew it as a resident vs. a brief visitor.