Thanks to everone who took the time to make a suggestion about how to solve this problem.
It turns out that if I want my compiled content files to be treated like content files (in that they get copied to the output directory of any other project that references my project), I need to create a target which runs before GetCopyToOutputDirectoryItems, and add the full path of the compiled content files to the AllItemsFullPathWithTargetPath ItemGroup. MSBuild calls GetCopyToOutputDirectoryItems for projects on which the current project depends, and uses the resulting file list to determine the files that are copied along with the assembly.dll. Here is the XML from my .csproj, just in case someone else has a similar problem.
I have a custom task called "ZipDictionary", and I accumulate all the files that I am going to compile in an ItemGroup called DictionaryCompile. My target, "FixGetCopyToOutputDirectoryItems" is executed before "GetCopyToOutputDirectoryItems". I don't do the actual compilation there, since this target can be called multiple times by referencing projects, and it would hurt performance. The target does some transforms to get the post-compilation file names, and then returns the full paths to all the files, since relative paths will not work when copy is called from the referencing project.
<ItemGroup>
<DictionaryCompile Include="Dictionaries\it-IT.dic">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
</DictionaryCompile>
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
<UsingTask TaskName="ZipDictionary" AssemblyFile="..\LogicTree.DictionaryCompiler\bin\Debug\LogicTree.DictionaryCompiler.dll"/>
<Target Name="BeforeCompile">
<Message Text="Files @(DictionaryCompile)" Importance="high" />
<ZipDictionary DictionaryFiles="@(DictionaryCompile)" OutputDirectory="$(OutputPath)">
<Output TaskParameter="OutputFiles" ItemName="DictionaryOutputFiles" />
</ZipDictionary>
</Target>
<Target Name="FixGetCopyToOutputDirectoryItems" BeforeTargets="GetCopyToOutputDirectoryItems">
<ItemGroup>
<_DictionaryCompile Include="@(DictionaryCompile->'$(OutputPath)Dictionaries\%(FileName).ltdic')" />
</ItemGroup>
<AssignTargetPath Files="@(_DictionaryCompile)" RootFolder="$(MSBuildProjectDirectory)\$(OutputPath)">
<Output TaskParameter="AssignedFiles" ItemName="_DictionaryCompileWithTargetPath" />
</AssignTargetPath>
<ItemGroup>
<AllItemsFullPathWithTargetPath Include="@(_DictionaryCompileWithTargetPath->'%(FullPath)')" Condition="'%(_DictionaryCompileWithTargetPath.CopyToOutputDirectory)'=='Always' or '%(_DictionaryCompileWithTargetPath.CopyToOutputDirectory)'=='PreserveNewest'" />
<_SourceItemsToCopyToOutputDirectoryAlways Include="@(_DictionaryCompileWithTargetPath->'%(FullPath)')" Condition="'%(_DictionaryCompileWithTargetPath.CopyToOutputDirectory)'=='Always'" />
<_SourceItemsToCopyToOutputDirectory Include="@(_DictionaryCompileWithTargetPath->'%(FullPath)')" Condition="'%(_DictionaryCompileWithTargetPath.CopyToOutputDirectory)'=='PreserveNewest'" />
</ItemGroup>
</Target>