Hola friends... I've watched the first vid a bunch of times and have some ideas.
Start off with cleaning the TB and plugs/wires if you haven't done them or are unsure of them.
Now.. let's analyze the vid (Scott.. please post a pic the normal shift table for this car to back up my ramblings.)
The car is at normal/not light throttle and not WOT. Let's call it 15-30% throttle. It appears to be in 2nd gear, it shifts into third and goes directly into TCC lockup. This isn't uncommon with some mileage on these trannies. Then the TCC unlocks as the pcm senses too much load for the power it believes the engine to be making....then it appears to go directly into 4th with locked TCC when it hits ~2k at the end of the vid.
I think the tune up is the right place to start based on OP's comments about it maybe being time anyhow. If this behavior continues after the tune up, unhook the maf, start up the car and see if it's still doing it. Ignition related, MAF, MAP and TPS all affect shifting.
If my % of throttle is totally off, and % is much lower then I would be concerned as to why it's not shifting into 3rd in the low to mid 30's and into 4th in the low to mid 40's. It appears like the trans is tired and sloppy, if you treated it nicely it might last for quite some time. I limped many many miles this same way.