You can do that, but you're gonna have a short hike to/from Lower Forge to Mullica River.
I usually use this map:
https://www.njhiking.com/nj-hiking-m...-trail-map.pdf
You can pick up a copy of this map from Atsion (if it's open) or Batsto Village.
It will be about 5.7 miles from Atsion to Lower Forge. Take the Mullica River trail (2.7 miles) to the Beaver Pond Trail (1.7 miles), which will take you to Quaker Bridge. Then head north for 1.3 miles to get to Lower Forge.
Next day head south to Quaker Bridge (1.3 miles), then take the Wilderness Camps Connector Trail (1 mile), then 1 mile south on the Mullica River trail so that's about 3.3 miles from Lower Forge to Mullica River. Next day, you can take the Mullica River trail right back to Atsion (5.5 miles). There are infinite ways to make the trip longer, but I would take the most direct route until you learn your way around Wharton State Forest. It's easy to get lost (trust me, I know all too well from getting lost there many times the last 10 years). At Thanksgiving this year, they had a hiker get lost and he had to swim across the Mullica River to get to camp (been there, done that). The problem is that the vegetation all looks the same and there is very little change in elevation (I think the tallest feature is Apple Pie Hill which tops out at 200 feet). You miss a few trail blazes and next thing you know you're two miles off course.
One problem you'll have is picking up your camping reservation. Atsion Ranger office doesn't open until April 1, so you'll have to pick up your permit at Batsto until then (offices close at 4 pm). You can either hike from Batsto (7.3 miles to Lower Forge) , or drive 30 minutes to Atsion and start from there.If you leave from Batsto, you'll have the same 3.3 miles from Lower Forge to Mullica, then you'll have a 4-mile hike the next day back to Batsto.
Some people don't even reserve a campsite, but I don't advise that because you're likely to meet somebody who has already occupied your campsite and has no permit. That happens often, and sometimes you just have to show them your permit and get them to vacate, or you'll call the state police. I've never actually had to call the state police, but I have found people in my campsite.
Here's another map I've never used, which may be of help.
https://www.state.nj.us/dep/parksand...al_reduced.pdf
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