Mystery vibration at 25 mph can't be diagnosed. It's not the front end!

Could a loose timing chain be the problem causing the shutter at 20 - 30 mph upon acceleration

No.

The lead mechanic swears it has to be in the ignition.

1. No, it doesn't. There may also be an ignition problem (cars can have more than one problem at a time) but the problem doesn't "have to be" in the ignition.

2. The ignition system on your car is stone-simple. Why is this guy standing there swearing about it instead of fixing it, if he's so sure that's where the problem is?

Pulled the plugs and noticed some gas on them. Could that be symptomatic of a loose timing chain

No.

I have pissed them off telling them to recheck the B&T

That's their problem.

If I could afford it, I would have them replace the timing belt/chain

There is no timing belt. Guessing at random parts to be replaced is a sure-fire way to waste money. If you cool off and decide not to sell the car, step "number zero" (first thing) you need to do is learn how your car works. Get the three books described in this thread and start reading. Otherwise you're going to be at the mercy of clowns like the ones you described at that shop over and over and over and over without end.

I've ended this madness.

Good!

At least they finished the brakes, tuned it and swapped out improper length spark plugs

What exactly did they remove as "improper length" spark plugs?