Mine reduced the self-pay fee because I was also having a hiatal hernia repaired, which was covered by insurance. I had to pay up front, and he was able to bill it and get it covered as one operation, so it seems I didn't need to pay all that anyway. I'm currently waiting on more than $5K in a refund from the hospital. Surgery was in April, and I'm getting the run-around. The whole insurance industry is a mess!
Also, while you're calling around, ask about supplemental BLIS insurance. My surgeon offered that for self-pay patients, and it covers a year of followup visits and any possible complications. Well worth the money. I think it was around $2500. Sounds like a lot, but worth the peace of mind.