I think I've found a lasting solution for the problem (credits to garymartynuk @ github)
This mod works by completely disabling SetPoint's handling of a chosen media key and letting Windows handle the input. For me it works flawlessly (MusicBee v3.1.6512 / Windows 10 x64 1709).
First of all you'll need to quit SetPoint and find your keyboard's configuration file. Go to C:\ProgramData\Logishrd\SetPointP\Devices\Keyboard.
In there you will see a bunch of folders, each containing an *.xml configuration file for your keyboard. There are a lot of folders (67),
so finding the right one might take some time, but it's worth it. I guess u could accelerate your search by opening SetPoint keyboard settings, modifying a keyboard key and saving the file. Then u could search for an *.xml file in windows and sorting the search results by modified date. The file you are looking for will contain the name of you keyboard in the beginning of the file (u can open/edit them with notepad).
I have a Logitech® Wireless Keyboard K360 and here's what the right file (2001001.xml) for me looks like in the beginning:
<Device DisplayName="Wireless Keyboard K360" Class="KeyboardDevice" Model="33558529" NumberOfButtons="18">
Once u are sure u've found the right file MAKE A BACKUP IN CASE SOMETHING GOES WRONG!
Press CTRL+F on your keyboard and search for HandlerSet="MM PREVIOUS_REWIND", HandlerSet="MM PLAY" or HandlerSet="MM NEXT_FF"
Each of these will be nested under a <Button> tag. It should look something like this:
<Button Number="786614" Name="Button">
<Trigger Class="ButtonPress">
<Param Button="786614" EventType="33554432"/>
<TriggerState Name="ButtonDownUp" HandlerSet="MM PREVIOUS_REWIND" HandlerSetGroup="SmrkndPreviousRewindTrackKbMs" HandlerSetGroupAddOn="SmrkndOtherKeyboard"/>
</Trigger>
</Button>
You can "disable" each button by commenting out the corresponding <Button> tag. To disable the previous track button u comment out its tag like so:
<!--
<Button Number="786614" Name="Button">
<Trigger Class="ButtonPress">
<Param Button="786614" EventType="33554432"/>
<TriggerState Name="ButtonDownUp" HandlerSet="MM PREVIOUS_REWIND" HandlerSetGroup="SmrkndPreviousRewindTrackKbMs" HandlerSetGroupAddOn="SmrkndOtherKeyboard"/>
</Trigger>
</Button>
-->
Basically, u add "<!-- " in front of <Button> and add "-->" after </Button>. Without the quotes of course. Do this for each key you want to "disable" (Play/Next etc). Disabling the keys this was lets windows handle the media key input, they work great in MusicBee and should continue working even after a MusicBee update.
Save the file, start SetPoint and enjoy your music with MusicBee =]