The middle of my front bumper, just under where the Pony is mounted, sags and creates a gap. Looking at other Cobras of the same year model, I don’t see the gap. See picture

I'm not saying you're wrong, but that picture is not great to help diagnose the issue, can you take better pics with more angles?
we have no idea what is under the bumper cover.
You can always count on me to have several naked MustangsI had to look for an image of a Fox with the bumper cover removed:
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Thanks @95steedamustang
See the portion of the bumper that looks [clean]?
Cut, shape, and adhere some of these:
They are made is several different thicknesses and some even have adhesive side, already.
You think one from here would work? https://lmr.com/item/LRS-17757B/1987-93-Mustang-Front-Bumper-SupportThat bumper support is for a pre 87. The 87-93 had the fibreglass bumper support like this...
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To me it looks like the bumper was trimmed too low (behind the cobra insert) and left no support to keep straight. That combined with black paint in hot sun has softened the plastic in the middle section leading to the droop.
I would try a board of wood or two as a spacer under the bumper cover (sitting on the support) and let it get hot in the sun and see if it straightens out on its own. Other wise you are looking at a replacement bumper cover.
So what you show in the link is a stock replacement bumper support. Your Cobra should already have this in place.You think one from here would work? https://lmr.com/item/LRS-17757B/1987-93-Mustang-Front-Bumper-Support
I looked really quick because it is raining here in GA. I do see the bumper support under there. But I also noticed where the top of the bumper meets the bottom of the grill insert, there is a gap. I guess, like you suggested, I will have to remove the front bumper cover which seems to be the front clip.So what you show in the link is a stock replacement bumper support. Your Cobra should already have this in place.
If you are looking to try and fix your existing bumper cover, I would remove it and reinforce the area below the cobra grill insert. From your picture it looks like someone cut the bumper cover flush with the top of the bumper. If you have ever looked up the instructions for installing a cobra grill insert it says to leave a 1/2-3/4" (I don't know the exact dimension off the top of my head) strip along the lower edge. This gives the opening and bumper cover top some structural support. A simple 3/4x3/4 angle that is bonded to the backside of the bumper cover should bring back the necessary structural support needed so you may not need to replace your cover.
Best bet if you want to save some money is remove the bumper cover and add some pics to this thread of the back side of the grill insert. We can talk and better explain from there.
ThanksA pool noodle shoved between the bumper support and the bumper would give good results.
They are cheap, easy to cut and fit.
Ryan
The front bumper cover removes very easily. If you own a Fox Body long enough you'll eventually remove it. That's the best to determine what's going on underneath there and will need to be done either way. If I recall, it's a total of 12 bolts.I looked really quick because it is raining here in GA. I do see the bumper support under there. But I also noticed where the top of the bumper meets the bottom of the grill insert, there is a gap. I guess, like you suggested, I will have to remove the front bumper cover which seems to be the front clip.