I've been tuning my adjustable gas block/adjustable gas key at the local paid rifle range and haven't had this issue. I had to significantly increase the gas flow to accomadate weak 223 ammo (pmc/reloads).

So over the weekend I went to the mountains to shoot. After a few rounds the 556 federal I was running started bending the brass during the feeding process.  The brass didn't bend at first though.  Typically it was happening after the first couple rounds.  It never happened on the first round.  There were also a large amount of light primer strikes with this ammo.  I've ran 223 PMC/ and 223 reloads which I haven't had this issue, but I wasn't running a crap ton of 223 like I was 556 (i didn't bring enough 223).  I'm assuming the two issues are related.

The brass didn't bend on the end of the casings, but in the middle there were gouges where the ammo tried to chamber unsuccessfully.

I'm using PMags and Hexmags. I have a ti carrier, taccom lw buffer, and wolf reduced power spring on a middy 14.5, Am I overgassed?  Rifle only has about 250 rounds through it.

It looked very similar to this pic

I would take all the lightweight, reduced power bullshit off and try again.  Your BCG is probably cycling too fast, not giving the next round time to come up in position to be properly fed, then the bolt is smashing into the partially fed round.

If those setback bullets are your reloads, your neck expander is probably too big.  What brand of dies are you running?  Some guys have mentioned having to reduce their expander some, because they are slightly out of spec/too large.

I'm using someone else's reloads.  The problem doesn't happn with the 223 pmc or reloads.  The problem occurs with the 556 federal ammo.

What about the light primer strikes?

It could simply be a result of the same or your hammer spring is installed incorrectly, or once again, it is that reduced power bullshit.  Do you have a standard spring on the hammer?  It could also be the reloads, if the primers are not being seated correctly.

I would never troubleshoot a rifle while using reloads.  Not even my own.

Those rounds with the setback bullets do not look like factory 5.56 federal ammo.  The brass looks like it has been tumbled and the bullets look aftermarket, and none appear to have a cannelure.

I forgot you said you had adjustable gas key and block.  I would open the gas key all the way, or use a standard BCG.  Close your gas block, and keep shooting, opening the gas block about 1/8 turn at a time, until the rifle properly cycles your preferred ammo.  There is absolutely no reason to have an adjustable gas block, and an adjustable gas key.  This is just an example of adding so much mall ninja bullshit to your rifle that it causes problems.

Reading comprehension fail.

OP:

1) Take the lightweight bullshit off.
2) Put in regular weight springs.
3) Turn adjustable gas block to lowest setting with factory 223 and then turn up until it cycles reliably.  
4) If you shoot some 556, turn back one setting lower -- and if it doesn't cycle then just turn it back up to the next setting.

I have a full power hammer spring on my Elftmann 3gun trigger.

If the hammer spring is installed correctly (check) then go back to square one.

Remove everything lightweight and go back to mil spec with the adjustable gas block closed and open gradually until you get the hot stuff, real 5.56 ammo functioning well.  That should be your goal if you plan to shoot 5.56.

Then try the low power stuff and see if it cycles.  If not, then open the gas block until it does.  Then check 5.56 performance.

All the extra stuff is irrelevant unless you are building a dedicated race gun that will run only one type of ammo and pressure, that you want to tune for.  If you do that, it may not handle the two ends of the spectrum well.  Goes with the territory.  Except for a dedicated competition gun, it's good to be a bit overgassed and be able to cycle everything you want to shoot.

I don't shoot 3G, but do shoot precision hand loads.  I'd rather have a little more muzzle movement and know that I can also shoot both full power 5.56 and my milder precision target ammo.