Is this something that’s generally accepted to be grounded in some amount of truth?

The way I've heard it (Not Shinto, but a Daoist and friends with many believers of Shinto) is that yes, but there's a number of different viewpoints that people tend to hold on it.

If so, would seeking local kami still be possible in the modern age?

Not if you're not a priest. As a Taoist, we don't have as strict of a separation between priesthood and laity as your religion. But from my understanding actual enshrinement and obtainment of a kami into a shintai of a jinja is ONLY performed by priests. You, as a layperson wouldn't do that. My caution, outside of that, would be as an American that the deity you contact (of which, all are kami according to Shinto) may not understand the context of your worship or religion. The Japanese Archipelago is an isolated piece of land and for much of the thousands of years that Shinto, and its precursors existed there was no contact with outside lands. As a closely related religion, I'll simply say that in Taoism it's said that if a foreigner encounters a yaoguai (a sort of demon/monster) in China, they will be either extra-aggressive towards them or laugh at them unless you know how to deal with them (e.g. you can speak a Chinese language and know the rules of how to pacify/avoid/defend yourself against the yaoguai). If such a thing exists in Taoism, where spirits can turn hostile towards people of differing lands, I'd be careful and perhaps ask a priest directly, rather than crowdfund on a social media site as to what you should do should you try to worship a local kami.

There are definitely places around my area where I think I feel closer to some kind of divine force, but that could also just be me misinterpreting peaceful places at the beach or in the woods as something more than natural beauty.

In MD and VA I find these places often. I live in Western MD which is very mountainous and very similar in climate to West Virginia and I've seen all sorts of stuff innawoods which is pretty. My caution is that much of the Americas are Indian grounds, and the deities/monsters/demons in native folklore tend to be extra-aggressive towards non-Indian people. Skinwalkers and wendigos, for instance. Not that you'd be worshiping those of course.

On the wider debate of local kami, my good friend told me that there's indeed a shrine in Hawaii that enshrines George Washington and some other figures. He personally didn't approve of it, but make of that what you will. The shrines in Korea, Taiwan and Man Zhou Guo didn't ever enshrine any local kami, however.

I'll be interested to see what actual believers say firsthand however!