"We quit burping a few years ago since it often was unsuccessful and took a long time. "
My experience relates to a Rotax 9 up to 920 hrs on which I never had "burping" problems. Technique certainly plays a part in obtaining a quick burp and I do understand, as the engine wears it may take a bit longer. Perhaps the additional 355 hrs on your engine changes things however I would not be comfortable flying my aircraft without the ritual burp before the first flight of the day.
As James Stricker said (above) there are other benefits to rotating your propeller/engine not just burping.
