As for stropping, my strop is an Illinois 127 and my main complaint is that it has shoulders along the edges that do not let the razor rest flat along the leather almost the whole length of the strop. It worked fairly well at first and would not let the razor touch my face without 4 or 5 passes on the strop but now I do not like to even look at the dagon thing.
Another thing that might help, is once you know you have your stropping technique down you should do more laps. Generally most people are doing 40-60 laps on the strop before each shave.