How to make afp://appleserver01._afpovertcp._tcp.local a fully qualified DNS name or IP address instead?
Number one, something might be wrong with your VPN, because everything should work as if you were physically in the office. You might want to check that.

Number two, I assume the remote machines use the wrong IP address when connecting to the servers. And if they are actually successful with some of the tricks you mentioned, you might have a few security issues (maybe caused by someone opening up too much of the network). But I don't fully understand the setup, so take that with a grain of salt.

Number three, I suggest considering a web server with all the necessary protections and storing the files there. Lots of such 'cloud' solutions are available, some for free, also with your own cloud servers, to keep the data local. With some technical knowledge, one can set it up with normal server software, too.

There are three main advantages: Access is possible without VPN access - much safer for some use cases. You can see and control what each person is doing on the server. And you can prepare to make the documents open online, which allows you to keep full control of them - no versions downloaded and then the laptop gets stolen...