You may benefit from cosmetic orbital decompression, where the eyes are set back but making the orbit larger to make more room for the eyeball to go back. It is an outpatient procedure.
Thank you for your pictures. It appears that your lower eyelids have a characteristic known as "scleral show". This can be a congenital variant, but also can occur with aging. The lower lid can sag because the natural attachments (i.e. the tarsoligamentous sling) that connect the eyelid to the skull bone have lost their integrity. In this situation, placing a small graft made of pigskin into the lower eyelid can support the lid back to an aesthetic position. The procedure also requires tightening of these attachments to the bone, a technique known as a "canthoplasty". In my San Diego plastic surgery practice, I attempt to position the lower eyelid so that it just touches the colored portion of the eye (i.e. the iris). It is important to be evaluated by a plastic surgeon or oculoplastic surgeon with special training in this technique.