There could be several reasons for the FTE.
1. Not enough gas pressure. If your rounds are marginally producing enough gas to operate the action, adding a heavier BCG may have made it a little worse. For the Blackout, a lightweight drive train allows you to better operate at lower pressures, so always look to go lighter in the BCG or buffer and weaker in the recoil spring.
2. Burr, or rough, or dirty chamber is holding the case in the action. Normally an AR is running pretty high gas and just powers through most chamber issues. But if this is a relatively low pressure target round, if may not be getting enough gas pressure to extract with a dirty chamber.
3. Headspace is off and dwell is not proper. If you did not change the bolt this should not be an issue. Check BCG for gas leak in the key. Also, make sure your gas block has not moved.
I have adjustable gas blocks on all my .300BLK ARs. That way you can set up for running with low gas pressure (like with subs) and turn the gas down for the high pressure stuff.
FTE is not usually a magazine issue. BTW, for running .300BLK I would either run straight GI mags (make sure they either have the new FDE GI followers, or MagPul followers), or the poly Lancers. The Blackout (bullet) uses more room inside the mag tube than the 5.56mm, so ribs that are just off from MILSPEC can cause them to bind. I see many places running sales on new Okay, D&H, and Brownells GI mags with the proper followers for $7-$8 all the time. Lancers can be harder to find and about double the price for the translucents.
That Range Officer had the right idea about bouncing the butt of the AR to use the weight of the BCG to extract the case. I have also put the charging handle on the edge of a table top and hit the butt to dislodge a case.
I have friends sometimes give me their old worn out GI mags. I take them apart, replace the follower and/or spring. I check the tube for cracks around the lips and the spot welds along the seam and throw out the ones with issues. I knock out any dents, clean and degrease them and then paint with hi-temp exhaust paint. I paint my floor plates some distinct color so I know which ones are mine at the range. I have also seen people use thin colored tape, like for auto detail painting, to mark their mags for whatever purpose, like which ones are .300BLK. You can also just stencil 300BLK on the side.