I don't think you need to rip up and start over.
esp if you get rain.
ripping up and starting over should be a last resort.
I would start simple and see where that takes you, it might take in some areas, but not others, but it could significantly reduce the amount of time or area you have to fully tear up.
Overseed it, run a chain harrow, overseed, run a chain harrow again. The local seed company will tell you the best mix (and you want a mix, not one straight kind) to use for your area.
Fertilize. Get a soil sample, take it down to the ag extension agent and they'll do the test and tell you what you need, go get that at the co-op and spread it.
all of this you can do with an ATV or your tractor.
Keep it mowed, when it gets to 12", mow it to 6" or so, (don't mow any lower, you want to keep the ground shaded) keep the weeds from going to seed and keep the grass from getting too tall.
In about a month to 2 months, after the seed is coming up, spray for weeds, to give the grass a chance to really get established. Ag extension will tell you what kind of weeds you have and what controls them.
by next spring, you should know what areas are coming back and what aren't and then you can go further. but I bet this would solve a lot of it.
KEEP YOUR HORSES OFF of it for at least this year so it can recover.
that's my suggestion.