You might consider the Olympic racewalking style at least in intervals. It's sometimes called "the really fastwalking"
It looks a bit goofy because the your hips have to move in order to keep the required stride "'only one foot on the ground at any time plus you have strike the ground first with your heel". Tons of videos on it. You also have to have kind of minimum movement or sway of your arms which may help with your rotater cup issues. It's a surprisingly good whole body workout not only strengthening legs but you core arms and shoulders too because you've got to move all of them so rapidly to keep a quick pace

Good luck!