Half an answer
I'm only going to try your rear derailleur issues. Biopace rings are notoriously difficult to keep shifting properly, so I am afraid I won't try to see what's going on there.
You don't say what kind of bike, though I will make an assumption by the mid 90's 7spd LX drivetrain that you're riding a steel hardtail. What's probably going on here is flex in the frame when you're on the bike, which is why it's ok in the stand but not when you ride it's problematic. This is where your barrel adjusters become your best friend. Start with like a quarter turn out, ride it, see how it feels, then another quarter turn, and so on. Hopefully that makes it better.
Otherwise you might want to revisit the limit screws, so that it rides a little closer to the spokes when you're in the largest cog. Once the shifters are indexed you won't have to worry about throwing the chain into the spokes, but take it easy in the beginning to make sure.
Sorry that I only half-answered half of your issue. Good luck.
I'm only going to try your rear derailleur issues. Biopace rings are notoriously difficult to keep shifting properly, so I am afraid I won't try to see what's going on there.
You don't say what kind of bike, though I will make an assumption by the mid 90's 7spd LX drivetrain that you're riding a steel hardtail. What's probably going on here is flex in the frame when you're on the bike, which is why it's ok in the stand but not when you ride it's problematic. This is where your barrel adjusters become your best friend. Start with like a quarter turn out, ride it, see how it feels, then another quarter turn, and so on. Hopefully that makes it better.
Otherwise you might want to revisit the limit screws, so that it rides a little closer to the spokes when you're in the largest cog. Once the shifters are indexed you won't have to worry about throwing the chain into the spokes, but take it easy in the beginning to make sure.
Sorry that I only half-answered half of your issue. Good luck.