My dilemma

Take it as a given that I want to keep my job. So how do I solve this problem? I can't do my job at the level of quality that I want, because other people have a say in what I do and how I do it. My boss asks for my advice, then either disregards it entirely, or just screws it up randomly. My battles with the PR department have been documented on this site, and every time I think I'm getting out from under their control, they fuck me in the ear with no oil.
I have a new VP, who has promised to "go to the wall" for us if we have a valid idea about how to do our work, who will defend us to the end for our vision of best practices. On the two occasions that I've had to test that resolve, he's caved, with the comment that one has to pick one's battles. So the result is that I don't believe in him or trust him and he's only been here for less than six months.

If asked for my opinion, what do I do? Do I give my best and honest answer, and wait for it to be ignored or gotten wrong? Do I give something less than the best answer, knowing that when PR gets wind of my point of view, they'll demand the polar opposite be done? Do I just smile politely and explain to my boss, that, well, he's the boss and he'll have to make those decisions? That I just couldn't (or won't) say?

That looks like (and is) passive aggression at its best, and a practice that is held in high esteem in this institution. While it works for damn near every incompetent I've had to deal with here, I suspect that I won't be allowed to get away with it. After all, the rules are different for me. Just look at the example of my office and the way I had to bend the rules into an origami crane just to get the furniture configured the way I wanted it, whereas the rest of the team, and the other team all got to bully their ways into what they wanted with no discussion from above.

Working here is like working in a particularly nasty whore house. Nobody wants to marry you when you quit. After a certain number of years working here, nobody wants to hire you when you leave. You've been ruined for real work.

And I have passed that point long ago. By the same token, I have lasted so long here that I am firmly held in place by the golden handcuffs. Offer me a job at the same salary, with the same benefits, and with a marginally more competent group and I would jump like a flea off a dead rat.

When I talk to other employees, we are all in the same place: held together with anti-depressants, cigarettes and alcohol.