The answer to the all-time leader in home runs by a catcher comes from Chuck Rosciam of the Encycolpedia of Catchers, but it's not at straightforward as I expected. Chuck explains that Fisk holds the "record" according to the SABR HR Encyclopedia at 351, but...
Fisk apparently holds the Record with 351 (out of 376 hit), BUT five of those non-catcher ones were hit between/during position changes. That is, Fisk's last defensive position was catcher in a game, then he came to bat and hit a HR and then he took up a different position in the bottom of the same inning. My logic tells me that he was still a catcher and that he didn't change positions until after he hit those five. That would make his Catcher-only total 356. However, there are 3 games in which he started as a non-catcher, then changed positions during the game with a HR being hit between changes (same rule as previous) and was WRONGLY CREDITED with a homer as a catcher. Now subtract 3 from 356 to make his Catcher Total = 353. Piazza's HR's as a catcher I believe stand at 342 unless he hit one in the past two days. That means that he needs 13 more to hold the record, which he will easily do plus some this season.
It gets kind of complicated. Besides as Chuck mentions, Piazza will obliterate the old "record" anyway, barring some catastrophe. So it won't matter by the time he retires if they count the home runs he hit just as a catcher or they count them all. He will still rank number one among all catchers.
By the way, my friend Mike informs me that the venerable NY Post did notice that Piazza hit his 350th home run but mentioned it just in passing:
"Obviously we got some bad news," said Mike Piazza, who went 2-for-3 with a double and his 350th career homer. "We're gonna have to persevere, scratch and claw and work hard.
"It's a tough time for us."
Wow, poor Mike didn't even get to enjoy it. I hope Alf took him out for a beer or something.