After getting the recordings I shortly got a message from the BoS knight, but
now, over four in-game weeks later I have not heard from this April character.
(The wiki says the second message from April is supposed to come immediately
after first message)
Is there some sort of glitch where you only get one upgrade bonus offer?

Did you ever do anything to upset to Followers of the Apocalypse? One recording should actually interrupt the other. They're part of the same thing.

I'm not aware of anything I did to upset them. I spoke to Gannon, Farkas and the ghoul woman briefly at
the fort.
I inquired about Farkas' quest but declined to undertake it right then. I don't know if that would upset the
brotherhood.
The message was solely from the Bos knight and the quest log only mentions finding him. April doesn't
appear anywhere in world at this time. I'd rather have the gun upgrade but I might as well visit the knight
and get this quest over with.

Yea, the message I got from the BOS knight was interrupted by April (Followers), so it was one message. You may have done something to have made them mad at you.