Yes, your scleral show can be reduced. A lateral canthopexy won't likely be sufficient. Without performing an exam to see how tight your skin is it is hard to tell how involved a repair may be, but you would likely need recruitment of skin from your mid face area then supporting the lateral canthus and mid face laterally to reduce the retraction at the outer corner. Sometimes this will improve to a certain degree as you get muscle strength back following your initial surgery. Internal eyelid grafts can also help "push" up the lower eyelid. This can be a complex issue that you should be in contact with your primary surgeon. I would suggest while you are waiting to do lower eyelid massage by pushing upward on your lower eyelid to help stretch the tissue and to lessen cicatricial (scarring) changes.
Your eyelids are severely compromised by your surgery. You have big eyes and the scaring and motor nerve weakness created by your surgery has caused the cantal tissues to undergo stretch back. Doing a lateral canthoplasty will shorten the eyelid and pull the lower eyelid further under the curve of the globe. The lower eyelid follows the shortest path on the globe and this will be lower on the eye surface. This situation can be fixed but it takes far more than a couple of stitches. That is required is vertically and horizontally lengthening the lower eyelids. To do this the cheek needs to be vertically lifted to recruit more skin back into the lower eyelid. I hand carve an ePTFE rim plant at the time of surgery which is fixed to the orbital rim and serves as a place to permanently support the cheek. Typically hard palate or an alloderm graft is used behind the eyelid to horizontally lengthen the lower eyelid and control the shape of the eyelid. You can read more about this on my website.