This occurred in a game officiated by NCAA rules, but I'm interested in the Fed point of view too.

3rd down, seconds to go in the 1st quarter. QB receives a shotgun snap and takes one step to the left, when the whistle blows loudly (ending the quarter). QB, and everyone else, believe the play is over. QB takes 2 more steps. DE, rushing past the line, actually makes a great play in avoiding the QB (even though he didn't have to). No one blew their whistle.

Then QB tosses the ball back toward the LOS. No receivers in sight and the ball didn't cross the NZ.

Technically - incomplete forward pass.

But is this also intentional grounding? How would you / your crew have handled this?

What whistle blew loudly? You mean the scoreboard horn? Anyway, certainly not intential grounding. QB did not try to conserve time or yardage.

Yes - the scoreboard horn. Sorry for the ambiguity.

Unfortunately, we don't have rules dealing specifically with ingnorance and a lack of common sense on the part of the players, but as officials we are entitled to use common sense now and then. I agree with JDLJ. The QB did not do anything that would gain an advantage. I would call it an incomplete pass and let the players suffer the wrath of their coaches.

Signal incomplete pass.
Change ends and try to contact the clock operator to request he turn off the scoreboard horn.

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That's exactly what we called. Incomplete pass, no penalty.

Visiting coach was yelling at his lineman, who was maybe 3 feet from the QB, to tackle the QB. After QB lobbed the ball forward toward the line, he wanted this to be a fumble. After we convinced him that the QB didn't drop the ball on accident or have it knocked from him... he threw it forward (unfortunately, my linesmen used the words "intentionally threw it forward"), he wanted intentional grounding.

It was a bit on the absurd side, but being the rules guy that I am, I thought about the wording of the rule. The rule says it's illegal to do what he did "to conserve time or yardage". To me, this implies intent - he must be throwing it forward with the INTENT of conserving time or yardage (ie - avoiding a sack or stopping the clock) - which I think it's clear he didn't do in this case.

But I can see the case being made that the rule doesn't state intent - is says he can't throw the ball away from the vicinity of an eligible receiver "to conserve ... yardage"... which, since he DID gain yardage (the next play started on the other end at the original LOS instead of where he was standing), might have been in fact illegal.

It just got me thinking, that's all.