I think I've located a possible cause of my problem - the new fuel filter I bought (based on O'Reilly Auto Parts showing a Wix 33011 as "Matches: Briggs & Stratton, OE Part Number" when I searched for 691035!) is a 12 micron filter and that is way too fine for this application.
The IPL shows 691035 as the part number for the fuel filter and is shown by B&S as being a 40 micron filter, much bigger than the 12 I'm using so that might explain the fuel starvation.