Mustang Issues - 2008 automatic transmission not shifting

So I am driving my fiance’s 2008 Ford Mustang’s and the automatic transmission suddenly stopped shifting. It happened during a short trip: while going around 45 miles-per-hour in third (I think), I applied the accelerator to get up to highway speed and … nothing! The RPM shot up but the transmission refused to upshift. It seems to reliably handle shifting from first through third, but it refuses to engage drive, only spinning RPMs. It looks like it’s even willing to red-line. My car is has a manual transmission and this feels very similar to applying gas while in neutral.

Then the next blow: I pulled into a parking lot to check basic functionality and it seems like reverse is also affected. Although it’s occasionally willing to engage reverse, and once the transmission is engaged it seems to stay moving, most of the time it will not engage reverse and just allows the engine to spin. It’s possible that starting on a declines increases the probability of engagement, but it’s hard to tell.

I didn’t hear a noise at the time of the first failure, but I can’t rule out the possibility that I missed one. This is the first time we’ve had a problem with this transmission.

I took the Mustang to the mechanic at a 45MPH trot and the mechanic suggested checking/replacing the fluids to see if a filter was bad or if they were low, noting this was a good thing to try before actually looking into transmission replacements. It didn’t seem to have any impact and the mechanic acknowledged that the fluid looked fine flushing.

The prospect of paying for a new transmission is a bit daunting. Before I spend this year’s vacation fund on a brand new transmission I was hoping to find out whether or not there could be an alternative or more targeted explanation of what’s going wrong. Can anyone lend any advice or experience?

Thanks,
-Dan