Cheers for the replies! I finally got a chance to spend some time on this tonight. I checked the psi on the tires, cold this time. The back tire was low, 30psi. I inflated the tires back to 34 front/36 back. I took it for a ride and, though the shake isn't there anymore on the turns, it's still not tight beyond 70mph. But the rear air pressure helped greatly.
Monster4Lee, you mentioned back tire being an issue and since I'd been riding it a little too squidgy, there's a faint wear line that's formed on the tire that looks like it was made by a bulge between the rim and road. Maybe. It just seems to be the most obvious reason for the marking. I believe that's what Ronski was describing. The look of a "tire sideways against asphalt"? Overall the tires look fine aside from that rear wear line.
I took it back home and managed to take the weight off the front wheel and moved the handle bars from left to right and everything was moving smoothly. Nothing seemed to be catching anyway. I used a plastic carpenter's square and gave the front wheel a spin and I didn't notice any issues with alignment.
And Philb, I'm going to go ahead and take it to a shop so they can give it a once over, check the steering head bearings and forks. From what I've learned so far, I'd like to catch an issue before it gets really bad. The whole an ounce of preventative is worth a pound of cure.
Thanks again guys!