Total shit show, but barrel can be removed from the upper, and using a mill, go back in and remove the current welded mess, then re-due the pinning weld correctly this time around, so it flush with the OD of the barrel.

Also, welding is completed with tig welder, instead of mig welder, so very little clean up after the fact to flush the surface at the weld with the rest of the barrel OD.  Hence with tig welding, your intial light up will fuse the top of pin to top of channel, then use of the rod is just to fill the channel to the top of channel alone.

On a Mig or FCAW if you don't want to run a sheild, by the time you get on the trigger to start to feed the wire, and come off the trigger to stop the wire feed with just a quick burst on the trigger, your already have too much weld over flowing the channel isntead (like what you have now).

So really, would get on the phone with someone like Adco, to send the barrel (or complete upper if you don't have the means to remove the barrel from the upper) to have that mess cleaned up, and the FS pinned correctly in the end.

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As for room for the lock ring on a surefire suppressor to lock into place with the barrel now, very suspect if your not going to have problems with the weld that high.  
https://youtu.be/-MvBqBoRLR0

As for a civilian individual to be able to own a suppressor in CA, that's a different story in itself.  
https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=PEN§ionNum=33410.

Also, look into your CA state laws on the AR-15 as well.

Take a good look at most factory AR barrels and the barrel shoulders look like this,





So the chamfer washer that comes with the FS, resolves the inner edge problem that is not flat on most barrel shoulders, and has the FS bearing against the outer edge of the barrel shoulder where its flat instead.

As for indexing of FS, it all about the supressor tab on it, and that you want BDC of the barrel.

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Now the down side, and since peel washers are soldered type washers, really not the best to use when you are blind pinning a FS onto a barrel for supressor.  Really, since heat will be involved when you are blind pin welding, really don't want any washers or shim involved to start with (barrel shoulder steel tight to FS steel).

Myself, will face the barrel shoulder on the barrel to get it flat, take a light cut at back of threads to make sure they are not going to interfer with the FS threads (so the taper washer does not have to be used in the first place),  face the back of FS as needed to get the FS to Index  supressor lug BDC at 20ftlbs of torque, then drill for the blind pin channel, install the pin, tig the channel closed, then flush and re-blacken the new weld on the barrel in the end (read hard pressed to even see where the barrel was blind pinned to begin with).



To add here, looking at the direction that the washer was installed on the barrel, looks like the chamfer side what instead backwards, hence it's chamber side against the FS, and not the barrel shoulder.  Also with the slight gap between the washer edge and the barrel/FS edges, looks like the blind pin is what is indexing the two together, and not the FS torqued to 20ftlbs before blind pinning. Hence if this is the case, then FS is going to be come loose on the barrel over time, which could lead to a baffle strike.  So like I said, Total shite show that needs to be corrected.

Solid flat steel shims should not be heat effected, but crush washers and peel type shims that are soldered together, are not going to do well with the heat and retain the FS torque values.    The same can be said of the chamfer washer, since it is a concave type washer for the most part, with welding heat may effecting it.

Hence since I do have the machinery, may as well use it, instead of rely on washers/shim to index a Muzzle device when there is welding involved.Plus, clean steel edge to edge line (which is not even visible from a glance half the time) looks a hell of lot better, then a stack of washers/shims between the two parts in general to start with.

In some cases when DCM AR rigs did have to have FS (before all the evil ban feature crap), even they where faced to hand tight install on index without the need of shims to index them.  Hence back then when the rifle had to have one, FS was pulled during cleanings, and where just installed hand tight on the rigs so they could be pulled between strings to clean the crown during barrel cleaning as well.

So is shimming right or wrong, all depends on just how much of a perfectionist the builder is to start with.