In addition to "longest walk possible" are there any good guidelines for finding trails/areas in the southeast that are typically less crowded on holidays such as the 4th of July? State parks here in Georgia, and most of the States, become overcrowded and very loud on summer holidays.
My answer is not specific for a particular area or a particular date. I like to find trails, areas, that are less crowded in general, and estimate the seasonal pattern mostly on availability. Signs of less popular areas:
- A relative lack of photos on things Panoramio, Instagram, etc.
- A relative lack of uploaded tracks on sites such as Wikiloc and Everytrail.
- A relative lack of google hits for places uniquely along this particular trail.
- A general lack of information online.
- A lack of services in the area.
- Look through some of the websites listed at the answers to this opposite question on Travel Stack Exchange, which essentially asks what's hot right now. My most recent hike was at spectacular Børgefjell (photos) and I met nobody, and indeed, it's completely black on sightsmap, as is the part of Iceland I hiked in the year before (photos).
Of course, this has the marked disadvantage that it's also harder to find those areas at all. It helps to know the area, to get a good map that includes not only popular trails but also less popular ones, etc. In northern Scandinavia, I've almost never met another hiker in routes that I designed on my own (though in some areas I have frequently come across people fishing or hunting recreationally, unaware that a specific area had been recently recommended in a popular paper fishing magazine that I don't read).
In the U.S. you have a huge system of national forests. Many of these have extensive trail networks. Many have parts that are too rough for economic logging.
Places that are far from a major urban area are far less likely to be used at any time of year. Most people will be reluctant to drive more than a few hours for a 1 day event.
Take more time and go deeper
One report on Jasper Park said that of all visitors that got out of their car other than for a ski-resort never got more than a mile from their car. There are only a scattering of trails in Jasper that have much use that are more than 10 km from the trail head. (The Skyline trail is a notable one.)
My experience with Willmore Wilderness (Just north of Jasper) is that 90+ percent of all encounters have been within 15 km of the Rock Lake trailhead.
Time shift your day.
By default people get up travel to the trailhead, and start their walk. This means starting mid morning for a nearby location. If you arrive at the trailhead at first light you're several hours ahead of the Rush Hour.
I did the opposite, and due to various delays arrived at the trail head at 3 p.m. We met one party coming out, and saw one party fetching water from a stream for their camp.
Time shift your trip.
Depending on what you do, you may be able to score points by working on the holiday, and taking time off in lieu during the following week. This works particularly well for ski resorts, as midweek lines are a fraction of what weekend lines are.
Space shift your trip.
Example: In Alberta Calgary and Edmonton have different weeks off for spring break. Since many families time their winter holidays for this, it results in overcrowding nearby vacation spots. However, an Edmonton family willing to travel a bit further can hit one of the Calgary popular sites during a time when Calgary is still in school.
Example: Some holidays are different in Canada vs the U.S. Canada has the August long weekend. Our Thanksgiving is the 2nd Monday in October; You have Memorial Day, We have Queen Victoria's Birthday a week or two earlier. You have the 4th of July. We have Canada day on the 1st of July. If you live near the border you may be able to take advantage of this.
Take advantage of the off seasons.
Depending how tough you are/how well equipped you are many places have an off season. Canyonlands is hot in August, and can be bitter cold in winter. West coast parks can be very wet. Spring melt and the uncertainty of fall freezeup can be daunting. These can also be spectacularly beautiful. Instead of canoeing in August, try it in October, as the shorelines are fringed with ice. Hike the alpine country in fog and mist.