I now always play with double horizontal straps. This works perfectly with a castagnari lilly. I'd really recommend a castagnari lilly with horizontal straps to anyone suffering from shoulder problems. Not only do you bypass your shoulders, it also keeps your melodeon pretty immobile so people using the thumb-on-the-ledge style of playing don't have to exert too much pressure, which also protects the tendons of your right arm.
With heavier melodeons this double strap system is somewhat uncomfortable on your back and internal organs
. This is an old picture that I have already posted on this forum (-not my melodeon). I have now devised a better system for my new heavier melodeon, using two old padded backpackers straps and backpack clips. I'll never go back to straps over the shoulders.