I think your GPS is correct, not Garmin Connect. Edit-- the ride has a 1500 foot climb at mile 15, and a 800 foot climb at mile 29. Add a half dozen 200 foot climbs, and the rough total is about 3500. So the 4600 number seems high.

That looks like a great route.

I downloaded your tcx track from Garmin Connect, and imported it to My Tourbook.

Here's the elevation graph with a red line elevation correction. Each of those small red "hills" adds up, 30,50,80 feet at a time. My Tourbook shows 3156 feet of climbing, counting 3 foot differences. Garmin Connect probably uses a different set of elevation and mapping data, so it doesn't compare exactly.





Here are the track points in the middle of the big climb. Each dot is a track point, the uphill ones are close together, of course. The dot color is speed, green is fast, blue slower. See how the track drifts off the road. This would be one of the red spikes on the downhill. Even though the uphill dots follow the road, the road's exact elevation at any spot is calculated from the nearest elevation data points, and can't be perfectly accurate.





Mile 15.5 to 16.5 is Hayter's Gap Rd between N Fork Rd and Brumley Gap Rd. It looks flat on Google Terrain View, but shows a phantom 100 foot hill on the red track adjustment.



L is the 15.5 mile mark, R is 16.5