There is some ongoing development work to make the stand-alone Authenticator App synchronize with the Password Manager App (per the Roadmap), but that is probably the closest you will get to an “all-in-one” solution.
Your other alternative is to support the feature request that I mentioned above.
The amount of functionality that Bitwarden already makes available for free accounts is unparalleled in the industry, and in my opinion, the “all-in-one” aspect is a convenience/luxury, not a necessity. If some of your volunteers place high value on the “all-in-one” aspect, perhaps they would be willing to part with 20 cents a week for this convenience.