So how rapidly do you need to flip the dots?
What is being displayed?

 

It should update in a second and I don't think that is slow. As per the amperage, that will be the same with AC or DC. I would think DC will actually be higher.
Just for interest, have you seen this video?

I'm looking around a bit to see if there are any practical circuits on line....

 

I simply don't want it to take 7 seconds to flip them all. If they can theoretically be flipped individually all in half a second then that is what I'd like to shoot for.

Going at 60Hz seems to be wasting a lot of time. And to make up for that I have to flip more at once and now contend with pulses of 30 amps. That's compared to 2 amps to do one at a time and getting basically the same result. I am also now plugging my project directly into the wall instead of getting my power from a UL listed power supply.

I appreciate the idea but I just don't see how this is easier than DC. The only more complex part about DC is the power supply which I can just buy.

 

Running on DC is ok, but you will have a more complex driving circuit I think.
Have you got a driver circuit for all the coils worked out for DC?
And are the coils just 2 wires or 3 wires? I know your circuit shows 2 wires only, but if they were 3 wire coils it is a lot easier.
And I don't know where you get the 7 secs from.
You can switch 1 row or column each cycle and there are 50 (or 60) per second.
You do not switch 1 coil at a time, but all in that row.
so it will be 28 or 16 cycles, depending on how you drive it. That is about half a second max.

 

I'm not sure what you mean by 2 vs 3 wire coil but the pinout I have is exactly like that diagram. And I believe the circuit is identical as well.

 

If the coils were center tapped it would be easier to drive.
I just had a look at the web page that shows the commercial drivers.
https://flipdots.com/en/products-services/control-units-for-7-segment-displays-and-xy5-boards/
They run on 24V DC.
They are quite complex, and I don't think it is a simple thing to make.
What is the type number of your display module so we can see the actual data?

 

You do not switch 1 coil at a time, but all in that row.

The problem with that is the high peak current from the power supply as the TS noted.

 

I simply don't want it to take 7 seconds to flip them all. If they can theoretically be flipped individually all in half a second then that is what I'd like to shoot for.

Then the simplest circuit is probably MrChip's approach in post #9.