But honestly, I think your time would be better spent moving it to .NET Core. I've moved a few big apps, and while I wouldn't class it as "easy", it wasn't really that difficult, more time consuming that anything.
https://www.nuget.org/packages/Microsoft.Windows.Compatibili...
The idea here being that you can quickly move to .NET Core using the compatibility shim, and then incrementally work your way off of it. .NET 5 will support the exact same concepts, so it still makes sense to engage this task if you want to get onto the new bandwagon.
You can use multi-targeting to move parts of your code over to .NET Standard. So if you start with your base projects and move your way up, gradually your code will become compatible between .NET core and .NET Framework. This will help you remove any .NET Full Framework / Windows specific bits. Where you have to have things that are specific to each OS you can then just configure your DI so it will inject the Windows specific / Linux specific implementation.
For those that are not aware of multi-targeting here is a great article on it:
https://weblog.west-wind.com/posts/2017/Jun/22/MultiTargetin...
Part of what has made it so much easier is the new "SDK Style Project File Format". It makes manually editing the csproj file mostly easier than using the VS editor for the vast majority of tasks. Which, for better or worse, is necessary to get some of the latest features. Got example, you can enable most of the latest C# 8 features for .NET Framework (which officially is stuck at C# 7.2).