After you get your razors fixed you may want to reduce the variables by placing the strop on flat surface (e.g. table, countertop). Then all you need to worry about is keeping the spine of the razor in constant contact with the strop - the edge will take care of itself.
Ten shaves are not much, so you could try light abrasive on one of your razors only. 0.5u (microns) chromium oxide is fairly standard, but you can use diamond or other 'pastes'/'powders'. Sparing use is important both in application of the abrasive to whatever surface you use (piece of wood, even the back of your strop may work), and in refreshing the edge (by shave 5 you would have deterioration so 3 laps and test, if necessary do 3 more - this order of numbers).

Keep us posted on the progress - it's much more difficult to do it over the internet, but chances are your issues are solvable.