It is the Stop Limits that drive the stock price down, the highs will sell as it goes up if the volume is there.
Stop Limits are the worst thing to do if you are trying to hold on to your shares. MM's always drop down and grab those Stops then head straight back to where it was prior to the Stop Limit.
The answer is use Limits and look for a window of opportunity when orders flow in on L2 and get the ask price for your shares instead of the Bid price. Any trader will know this but without L2 they won't.