There aren't many situations that are what the OP describes as "sunny 22," so I am guessing that at least one stop, and maybe more, of the difference he is seeing between the two readings is due to the brightness of what the reflected meter was pointed at.
Incident readings simply should not match gray card readings, no matter what diffuser attachment is on the incident meter, for the reasons mentioned above. If reflected meters were designed to produce 18 percent gray, then they would match. But they are not designed to do this. Gray cards will cause underexposure unless you open up a bit from the reading they give you.