Do I have the right exhaust hangers on the car?

Look underneath on the left side.
No matter what plain jane engine your car started life with, it came with the left exhaust bracket welded to the floor pan.
The part that comes straight out with a hole in it is for the brakes.
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On a dual exhaust car a second bracket was bolted on the right side.
We can see in your first photo that your car doesn't have one.
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Whether that will help you is hard to say from this side of the screen, but when you're under there you may be able to judge the relative positions.

TTI's hangs their muffler brackets from the seat belt anchors. That's looks like where your car's right exhaust hanger is welded.
I don't think that will help you. I agree with Demonracer. With the system welded, it needs to be cut, repositioned and then rewelded or clamped.
As far as hanging goes, there are many hangers that can be made to work. I do like the factory style but no reason to limit yourself if they aren't going to work out.

Notice the factory muffler inlets are offset. That helps keep them away from the driveshaft. Sometimes (always?) that inside corner was dimpled or flattened for more clearance. Shouldn't need to do that with a shorter muffler and/or custom run pipes.

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