Thanks for finally answering the question about starting in first. Although you didn't actually say that, you just said "with the clutch pulled in." I"m assuming it was actually in first when you cranked it with the clutch pulled in. . . . . And you didn't mentioned if the bike tried to move, even just a tiny little bit.
And as for your continued insistence that it shifts in other gears so it isn't the clutch, let us repeat the statement that
[SIZE=24pt]a trannie with dogs rather than synchros will upshift perfectly without clutch action.[/SIZE]
(And it will downshift perfectly with just a half-pull on the clutch, an obviously incomplete release.) The difference in going into first while stopped is that the output shaft isn't moving, so engaging first gear is done by the dogs catching the receiving holes as they spin by, and bringing the input shaft to rest. If the clutch doesn't disengage correctly, that can't happen.
Something else that can cause this is trying to shift gears when the bike is not even running. Very bad mojo!! Never kick a bike's shifter with the engine stopped. I've seen a guy who for some reason or another developed a habit of parking in neutral, then kicking to first when he got on the bike, then starting it. Forks will bend.
Back to your situation. I think the guy at the dealer knows there are no synchros in a motorcycle box. He's gauging what you know about it, so he can see how big a ride he can take you on. That's the reason to find another dealer. Find another dealer, start over with him. Tell him you have trouble with first from neutral while stopped. Tell him you know that some FJRs have had a sticky clutch problem. Tell him you wonder if yours has had this. An honest and reputable dealer will know what all of that means. And please stop telling us it's not the clutch. Unless the shift fork was installed bent, there's nothing else it can be. Really. (It's entirely possible it isn't the clutch any more, but a bent fork. But that fork got bent because the clutch wasn't working, if it's a bent fork.)
BTW, the link RadioHowie sent you is a good one, but the animated shifting gearbox at the bottom is automotive, with synchros, not a motorcycle box. The very first animation, with pegs going into holes, is how a motorcycle transmission works.
One more thing to ask about the bike and its performance: How does it do when downshifting into first before you get stopped? While braking for a stop light, kick down through the gears, all the way down to first. Does it take first easily while still moving, or is it still difficult to get first? You don't need to release the clutch between shifts, just kick-kick-kick-kick while braking and holding the clutch lever.
If it has difficulty getting first while moving, then it's probably the shift fork. Two things can bend a shift fork. Bad clutch action, or shifting while not running.
If it gets first easily while still moving, but not while stopped, then the clutch is the ONLY piece on the bike that can cause that. Your insistence that it's not the clutch because other gears work is totally and completely invalid. Really and truly. I'm not the only one to have said so, either, so don't dismiss it because it comes from me. I'm trying very hard to get past your attitude and help you figure out the bike's problem, but until you accept that we do know what we're on about, then we can't get very far.
(BTW, I'm one of the guys that agreed with raising the idle speed. That worked.)
(BTW #2: The clutch is easy to work on. Don't let some shop tell you about 6-hour labor times or anything like that. There's a cover to remove and you're there. Now, the transmission itself, if you have a bent fork: that's a different story. Engine comes out and the crankcase gets split. Big mojo there, much shaking of rattles and consulting of bones.)