For those who've chosen a particular endgame but want to keep Classical Radio. Suggestions and fixes are welcome, I've literally never used Papyrus before this.

The Plugin
~~~~~~~~~
Load this plugin on a save that's finished the main quest. Alternatively, if it doesn't work, pop open the console and run "startquest radioinstitute" (no quotes), which is pretty much what this plugin does anyway.

What it does is run this script:

ScriptName FixClassical extends Quest

Quest Property RadioInstituteQuest Auto Const
Quest Property MQ302 Auto Const
GlobalVariable Property RadioDCInstBroadcast Auto Const Mandatory

Event OnQuestInit()
    if (RadioInstituteQuest.IsStopped() && MQ302.IsCompleted())
        RadioDCInstBroadcast.SetValueInt(1)
        RadioInstituteQuest.Start()
    endIf
EndEvent

You can unload the plugin afterwards and ignore the compatibility warning, it doesn't add anything except the hidden quest to run the above script.

The Quest Fragment
~~~~~~~~~~~~~~~~~

Inside the quest fragment for that particular quest (Scripts\Fragments\Quests\QF_MQ302_000229EE.pex) are two lines that disable Classical Radio; the included quest fragment is the same as the vanilla game except with those two lines commented out, so the game shouldn't even disable Classical Radio in the first place. Testing it with a save prior to the moment Classical Radio is disabled shows that the action is in fact stopped by the new fragment, but testers are welcome.

If you just want to change the fragment .psc yourself (the one that's included with the game), disable the read-only flag (if set), open QF_MQ302_000229EE.psc and change:

;turn off Institute radio broadcasts
RadioDCInstBroadcast.SetValueInt(0)
RadioInstituteQuest.Stop()

to

;turn off Institute radio broadcasts
;RadioDCInstBroadcast.SetValueInt(0)
;RadioInstituteQuest.Stop()

and recompile. Put QF_MQ302_000229EE.pex in the right spot and run the game.