I have 26" Heavy Encore Barrels in 7mm Remington Magnum and 300 Winchester Magnum. There's not much use for them in Ohio, but the 7mm barrel came in a trade and the 300 WinMag was only $100 (with a forend!) at a yard sale.

Accuracy with factory ammo has been very good - the 7mm may be the most accurate barrel I own on any gun - but I have to physically lift the extractors on either barrel over the belt and then place it in each round's extractor groove in order to load them. If I just try to close the Encore with a belted round dropped into the chamber, it won't close because the cartridge sticks out too far. I have never had any extractor difficulties with any rimmed or rimless case with the gun.

Has anyone had a similar problem? Or is there something wrong with the gun or my technique?

None. Maybe your extractor is bent? Some extractors have a small flat spring installed......

IME Encores are pissy with rimless cartridges. Sounds like your problem is getting the case past the belt and engaging the extractor in the rim recess which is smaller than the belt ?

The design is like that used for rimmed cartridges, not positive like a Ruger No. 1. My 280 AI is so bad, I'm gonna convert it to rimmed by using 7x65R cases. I had a HighWall (original design) in 300 H&H that was also a PIA. Fixed it by converting to 300 Flanged (a rimmed, beltless 300 H&H). You could do the same as the flanged base is as big as the belt. You need to find a Smith with access to a reamer that will open up the chamber and then go thru brass forming.

Plan B would be to sell them off and buy a more appropriate chambering for where you hunt.

I have plenty of appropriate chamberings to hunt with. Also plenty of inappropriate ones to play around with.

Maybe someone installed the wrong extractor.
I've never had that sort of issue with my Encores.

Didn't have any problems with my 300 WM barrel other than recoil was impressive.

I have 300 Wby & 7 Wby Encore barrels with well over 500 rounds thru each with never an issue. Sounds like your extractor spring is either broken or installed incorrectly.

Sounds like the extractor could have some sharp corners maybe. My 7mm mag barrel was that way too. You may need to round them off a little.

I used to have a 375 h&h barrel for my encore. Never had any problems like that.