The local bike store might have a bike with 32mm or 35mm tires on it. They could put those wheels on your bike while in the store to verify the clearance, or just use a shop micrometer to measure the available space on your bike. If they had 32s to try, you could then see if there was room for 35s, which need only a couple of mm more on each side and on the top.

Some retailers use 700 x 32c to designate the size. 32mm and 32c are the same size.
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Riders on the GAP and the C&O canal trail have reported that 28mm worked for them. But I like wider tires, so I don't need to watch the trail surface very carefully. There's occasional soft spots with looser material on unpaved trails, and wider tires are more stable at those areas. I think the wider tires sit on top of the surface better, so they have somewhat better rolling resistance, too.

Don't forget to lower the air pressure with the wider tires. For a bike + rider around 200 pounds and 35mm tires, I'd try 45 to 50 psi front, and about 60 psi rear.

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Have a good time on your ride. The GAP trail is on my to-do list for next year.