Although to use neutral polish for cleaning works pretty well (as MPS has recommended, presumably on the recommendation of Mme Berluti), it needs quite a bit of elbow (or index finger) grease. For larger scale stripping jobs, Mme Berluti recommends vodka, I'm not sure if you need a special brand or if any old vodka will do. But for polishing shoes (again, according to Madame) only Dom Perignon champagne will do. If you prefer your Stoli chilled and served in small glasses, use white spirit or surgical alcohol. Dampen an old cloth with it and it will take the whole gunk off in next to no time. Once you have stripped the shoes give them a good coating with leather food or neutral cream (the soft stuff from glass jars, not the polish from flat tins.) Then you can inspect them (use a magnifying glass if necessary), if the cracks are in the leather or have been removed with the old polish. It is possible that your Church's shoes were made from corrected grain leather (bookbinder), which looks very shiny when new but does not wear well. If the cracks are in the leather, there is not very much you can do; apart from regular shoe cream, as to make the problem not worse.