I haven't looked at http4s's custom collections in particular, but I can offer some general advice in this area.
Very likely you will need some Scala-version-specific sources. (sbt makes this surprisingly easy to arrange.)
It is not usually necessary to copy-and-paste sources wholesale; it's usually possible to get by with just a few aliases and forwarders in version-specific source files.
an example: https://github.com/scala/scala-xml/blob/master/shared/src/main/scala-2.13/scala/xml/ScalaVersionSpecific.scala and https://github.com/scala/scala-xml/blob/master/shared/src/main/scala-2.11-2.12/scala/xml/ScalaVersionSpecific.scala , which are wired in to the build here and used here
another approach is to take on scala-collection-compat as a dependency. this can require less work on your end, but has all the downsides that adding dependencies always has