I have similar problems trying to lean the engine on my PA-38. Very, very careful adjustment of the mixture control will result in a leaned engine and an improvement in fuel consumption but, as you've discovered, 1/8 inch too much on the mixture control and the engine damn near stops. The rpm peak is rather small and Danny Boy's method seems sensible to me.
I flew Beccles - Wickenby and back yesterday, mostly at around 5700 feet and managed to lean it enough to bring the fuel consumption down from 24 lts/hr to about 21 lts/hr. It does take a bit of practice to get it right though!