As a few here have already pointed out, clipping Parker's wings wouldn't do anything for your main intent of being able to take Parker out and about. A properly done clip would still allow him to catch a gust of wind and get taken quite far rather quickly. There have been a number of cases on this very forum where a clipped bird has flown off and gotten lost. You'd be surprised how far they can go with clipped wings.
And as you've mentioned, Parker is prone to being startled. Outside, there are any number of things that might startle him. Loud noises, moving cars, or even the glimpse of a hawk or falcon flying overhead. I remember my mother teasing me one day about why I even bothered to harness Maya for a walk we were taking, since she "never" flies. Not 5 minutes later she took off, startled by the sudden flight of a bunch of crows from a nearby tree. And mind you, Maya isn't easily startled nowadays. (My youngest son waving a brightly colored balloon around while sounding off with a battle cry as he ran past her tree stand was the last thing that managed to freak her out indoors.) But the outdoors is just a whole different animal.
Is it possible to clip a bird to the point that even such wind-aided flight would be impossible? Absolutely. But such a clip would be cruel and dangerous. Because those kinds of clips cause the bird to fall like a rock. Unable to slow his fall, the bird could potentially break his keel bone. (I know this isn't an option you'd take, Chris. Just laying everything out, here.)
If you're looking to get Parker some Vitamin D, April's suggestion of the pak-o-bird is a great option. As is Dani's and Uglow's suggestion of a smaller travel cage. (This is what I do as well, btw.)
Remember that, as far as Jolly is concerned when it comes to harness training, I'm in the same boat you are. (Which is weird, as I'd have bet a significant amount of money that he'd have been the easier of my two ekkies to train.) It's frustrating, I know. Jolly would LOVE going outside! But I think we just have to remain patient. Some birds just need longer to accept being harnessed.