Who suggested that the chain was too wide? Have you ever changed the chain? More likely that the RD just needs adjustment. Might need a new cable.

Top gears are the top ratio gears which will be the smaller rear gears on the bike? Or are they the low ratio gears which are the biggest rear cogs on the bike? Or are you describing the gears on the crankset?

If you messed with the two limit screws that are side by side, they don't do anything for your issue. They are only limits for how far the RD can move. If anything it's the barrel adjuster or inline adjuster you should probably have tweaked. But that isn't necessarily your issue. There are other things it could be.