Can I persuade my doctor to perform a sleeve instead of bypass?

The answer is probably no. A properly performed Sleeve gastrecyomy with no narrowing and no retained gastric fundus may resolve acid reflux. Weight loss after sleeve and other underlying mechanisms like improved gastric emptying contribute to improvement in acid reflux. A recent study has proved that reflux resolved after gastric sleeve surgery and new onset reflux after gastric sleeve is rare. Previous older studies have shown that acid reflux disease may get worse after sleeve. However, this may be related to a narrow sleeve or Incomplete resection of the upper part of the stomach called gastric fundus.Gastric bypass surgery is an established anti-reflux treatment and is a good option. However, it is more invasive and contraindicated if you take aspirin like productsHope this helps, 

Be sure to tell your doctor that you take NSAIDS chronically which in my practice is contraindicated for a bypass.  NSAID use with the bypass is in the top 3 causes of marginal ulcers.  Your doctor is probably concerned with your GERD and hiatal hernia worsening with  the sleeve.  The sleeve is a high pressure system and the bypass is a low pressure system which is a good argument for the bypass.  You need to understand that a sleeve could potentially lead to worse GERD.  I have not found GERD to be as much of a problem as we had initially anticipated with the sleeve.  Losing weight and eating smaller portions can often alleviate GERD symptoms.With that said, if you have Tricare, it only covers the lap band or bypass.  The sleeve is still considered experimental for Tricare insurance.  You might be able to get the sleeve approved if your insurance coordinator and surgeon are willing to make the argument with your insurance.  Additionally, if your BMI is <40 without a comorbidity, I question whether Tricare would cover the procedure. You do want an experienced sleeve surgeon to do your operation and if your surgeon is not doing these then perhaps you should consider paying for it with a non military surgeon or waiting.