340

Are you sure your rings are broken in ?
Also you aren't running the 273 crank in a 340 are you ?
273 anything on a 340 is no bueno.
Anything? Uh, no. There is nothing inherently wrong with running a 273 crank in a 340, and people run 273 rods all the time- they make for a much lighter rotating assembly. DC offered prepped versions in their catalog and recommended them in their build guides. And name one builder that hasn't used some form of 273 rocker arm on their builds.
I'm sure the OP's use of the 273 crank was due to the smaller crank pocket needed to run the early 904.

OP, I think your plug situation is a combination of things, including carb tuning (I'll assume for now you've got the carb set up right- choke working correctly and not stuck closed- and at least ballpark idle mixture and jetting, and your J heads don't have worn out valve guides), but not the least of which may be your ignition system. My admittedly somewhat limited experience with Pertronix conversions has been, well, not at all good. Despite claims, they just don't seem to deliver a consistent, hot spark. Too many issues ranging from quality of components to just being somewhat of a compromised design, only marginally better than the infamous "Skip White" all-in-ones. MSDs are a step up, especially if you can find one of the older units new or used. My favorite is the old reliable Chrysler distributor with an older Chrome box- in nearly 50 years I can count on 2 fingers the number of ballast failures I've had, and one of them was my own fault. The HEI converted Chrysler distributor is a real close second. Neither has ever let me down, design wise (just don't use cheap Chinesium parts here).