I just ordered a Bergara B14 HMR and am now looking at glass in in $400 range for this gun. The furthest range I currently have access to is about 880 yards and don't see myself going much further than that any time in the near future.

I am currently looking at the fixed 12 and 16x SWFA SS series, the Vortex Diamonback HP 4-14 and the Primary Arms 4-14 ACCS.

I like the simple mil-dot reticle of the SWFA and Diamonback and find the ACCS to be very "busy" but it has a lot of features for the price. Any other optics I should look at in this range?

SWFA, Weaver, Leupold

All make good mid-dollar fixed powers (yes, even weaver)

Vortex and Bushnell both offer good discounts for vets through experticity.  The Bushnell 3200 fixed 10x is available very cheap.

I would not use a Vortex offering beneath the Viper line.  Of the scopes you listed I would take the Super Sniper.  The Weaver 3-10x40 is an excellent option in this price range.
https://www.natchezss.com/weaver-grand-slam-tactical-rifle-scope-3-10x40mm-mil-dot-reticle-matte-black.html

Personally, I would bust your budget and get one of the Weaver Tactical 6-30x56FFP optics from Natchez while they're on clearance. 
https://www.natchezss.com/weaver-super-slam-tactical-rifle-scope-6-30x56mm-34mm.html

The big problem with budget glass for your application isn't optical clarity, but reliable tracking.

Many budget tactical/LR scopes will fail if you work the knobs much.

My vote goes to the SWFA SS for that reason. Erector assembly is a tank.

right, and watching this video has steered me more in that direction, granted it was just a once around it was pretty spot on.

If you have the vet discount, the vortex hst comes in near your budget for the 6x24.

Interesting.  I've never fired the square.  Do you truly need to shoot at each point, or if the rifle is locked in a rest, can you simply dial the square and see if the crosshairs move to each correct point?

The point of aim remains the same throughout, You pre measure then dial in the adjustments per the measurements. IF it tracks properly the rounds should impact the dots per the measurement and adjustments that you did.

If you sign up for the Experticity vet discount, the Vortex Viper HST is like $430.

I'm a big fan of fixed power optics.  I'd probably go with the SWFA fixed 10x or 12x...

Bergara B-14 / SWFA 12 x 42 / .308 - LRSU 1,200 yard milk jug challenge - LINK  

<shooter gives rig rundown @ 3:20>

They also used that same gun for a 1 mile milk jug shot in 7 shots and that wasn't even the HMR, that was the standard B14

Yeah, I saw that one too!...  Impressive!

SWFA 12x hands down. Tracks great. Used it for me 1000 under $1000 build and long range school last year.  Bangsteel.com.  Dan Newberry recommends it to anyone on a budget.  I actually had my rifle fall out of the safe and bend the top turret.  Swfa replaced it no questions asked. I even told them what I did.

I Have the Diamondback hp 4-12x40 too.  Good scope but you aren't going to adjust the turrets to shoot long range.  Ain't going to happen. It's my hunting scope for my 6.5 and the bdc reticle lines up really close on every hash out to 500 yards.  Pretty good in low light. I abused it pretty good last year and it held zero great.

Just had the PA 4-14 and sent it back. Clarity was crap.  Cabelas has the viper HS long range for $399. Considering that to replace the PA.  Really want a variable for another hunting rig.  Also looking at the viper Hst.  Trying to find out how to get the veterans discount because if I can get it for $430, I will buy it right now.

So how does this Experticity thing work now?

It's like an online shopping mall with a bunch of vendors within the site.  You browse and order from within the site.