What is the overall success rate with a sling using pig tissue for pelvic/uterine prolapse in the hands of an experienced doctor?

Unfortunately... Not any better than a traditional suture repair in the hands of an experienced doc according to most of the data. Some reports even demonstrate higher failure rates. These types of grafts have been around for longer than the mesh grafts. If they were better the mesh would never have been pursued. Sorry.
Around 80 percent. Successes rates for the treatment of pelvic organ prolapse with biological grafts very depending on how you define failure. Patient symptoms vs measurement on exam, etc. My success rate with sis ( pig ) graft is about 80%. I normally quote a 20% failure rate by 3 years with sis. Many factors must however be considered . Age of patient, degree of prolapse, tissue health, prior surgey.
Would need more info. Consult a gynecologic surgeon or urogynecologist. A surgeon who performs surgeries for prolapse frequently is important. Don't be afraid to ask. Look for a surgeon who does at least 2-4 prolapse surgeries each month and has done 50 or more in the past at a minimum.