In all of the interviews I've been to recently, the interviewers continue to press me if I focus on their company and don't say something about why I want to leave my current employer.
After a particularly bad interview, I did start practicing for these types of questions and I'm getting better, but that's still relative. Part of the problem is that I've been in the toxic workplace so long and I'm so desperate to get out of it, that thoughts of escaping push to the front of my brain while I'm in interviews and I either blurt out something I shouldn't  or I just freeze up (think deer in headlights), typically a combination of the two which is even worse.
 I don't blurt out anything quite as bad as "my current boss is an ass", rather things like "My boss doesn't believe in bug trackers and I think they're extremely important." So far so good, right? But then there's a pregnant pause and I catch myself blurting out, "At least a client threatened to take away our business if we didn't start keeping bug records, so now we have 3-ring binders and paper forms to record our bugs. But that doesn't do any good when the same bug is reported multiple times in every binder and the boss doesn't actually look at the bug reports or give anyone else access to the code." At which point the looks on the interviewers face tell me I've blown it again. (Very true scenarios about our bug reporting and my idiotic blurting out in an interview.)
Maybe it's how you're saying it, and not what you're saying? Is there somebody you could practice with? Somebody who could point out body language or tone of voice or other cues that could be giving interviewers the wrong impression about you?
One other possibility...
Maybe round out that story by mentioning how you (or the team you were a part of, even if you weren't the lead person on the effort) tried to solve that problem in a constructive way. "We gave our boss a presentation on three popular, low-cost issue trackers that we tried and liked... to no avail." Surely your next employer will make some decisions you don't agree with - they're wondering how you will handle them!
I have to admit, I never considered trying to recover after I get the "look" from interviewers. In fact, I had provided multiple recommendations on bug-tracking software, to include setting up demo servers for several different packages (because of those demos and related discussions, our interns started using both bug-tracking software and GitHub for their projects - so that was a definite win).
> I certainly think part of my problem is the how I'm saying it.
If you truly are coming off awkwardly, what's the real problem there? The problem is this: the interviewer is wondering, "How is this guy going to interface with the rest of the team here if he's this awkward? Does he even know he's awkward?"
So... you can address both of those unspoken questions head-on. Mention that you tend to get nervous in interviews and when meeting people for the first time and that it's something you overcome fairly quickly and that you tend to develop really good working relationships with coworkers. (Because that's certainly true from what you've said)
> I wish I had somebody who could do this for me!
> In fact, I had provided multiple recommendations on bug-tracking software,
> to include setting up demo servers for several different packages (because of
> those demos and related discussions, our interns started using both bug-tracking
> software and GitHub for their projects - so that was a definite win).
> ... you might not be coming across as awkwardly as you think you are ...
I have no doubt that I am.
> ... you can address both of those unspoken questions head-on ...
I honestly never considered this, but will in future interviews!
> If you live near Philadelphia...
> Is there anybody non-technical that might help you? Siblings, parents...?
I do participate in a ton of meetups. Would it be appropriate to ask a peer from a meetup group to be a proxy for an interviewer?