2010 Jetta Slipping Out of Reverse

Hey guys,
I'd been told previously that my flywheel would need to be replaced here at some point, and it seems like that point may be sooner rather than later unfortunately. Within the last week, I've had my 2010 Jetta slip out of reverse twice. Is it likely that this is the flywheel? It also feels like it's slipping sometimes at slower speeds, but it's never kicked out of gear going forward thankfully.

If it is, would you guys go ahead and replace the flywheel? (Automatic) or would you be looking at ditching to pick up a new car.

Is this something you'd do yourself if you've never really done any transmission work before?

Any tips or ideas would be a great help.

Thank you all!

Also, I'm in the Louisville area of Kentucky now. It appears that Skunkwerx is out, and Paramedick doesn't work on Flywheels. Does anyone know of a reliable place to get this swapped for a reasonable price?

If you are OK driving a few hours to get it worked on, Matt Ford has a shop in Knoxville that specializes in VWs.

Thanks @MikeH31324. I'll take a look at it. Definitely wouldn't mind to drive a few hours if he wouldn't charge out the ass for it.

Every quote I've found to do it will be around the 1k mark, unless I do it myself at a DIY garage here. Then I may be able to get it out for $600 or so between parts and the garage membership.