Option 1: Move your range a couple of inches to the left or right, so you can send the pipe up between joists. Option 2: Use a different kind of range hood--one where the whole thing goes all the way to the ceiling, or one you put cabinets over--so that you can send the pipe straight up between joists(i.e., off center relative to the hood and the range) without the off-centeredness being visible. Option 3: Like Don says, elbow around the joist. Or, if this is just one joist you're proposing to cut, learn everything you can about the method Chrisk327 describes (or hire a reputable structural engineer to tell you what to do), and do that. But if you go that route, DO NOT jerry rig it, DO NOT just try to wing it or figure it out as you go--that joist is literally holding up the floor and/or roof above it, you don't want to get this wrong. Not to mention, an improperly supported joist can fall down into your kitchen... and fixing that ain't cheap. Which of those options seems like the wisest course to you? Assuming #1 isn't possible--maybe the counters are in the way--I would go with #2. Having to put the range hood you have on eBay and get a different one is a lot cheaper and less time and hassle than having to take a crash course in residential structural engineering, buy the materials and tools, chop into a supporting beam of your house (and hope you don't cause permanent damage), and then fix the ceiling up again around it.

"The pre-made repair plate is quite thin and it's made for a small hole in the joist, not for most of it cut away. So no, they haven't done calculations for me. " Did you read the listing? It is designed for more than the maximum cutting, but yes, it still has limits. If you need a PE sealed fix to satisfy an AHJ, open your wallet. It should only be under $1,000 to examine the joist, determine the loads, and design a fix. PE stamps come with liability, so they are not used for free. Or you can just guess (but be careful, your comment about "repair plate is quite thin" indicates you may be in over your head. Even thin metal has surprising strength when formed and applied correctly. All the metal is fixing is the maximum shear load the joist is designed to carry so it does not need to be especially heavy if it is formed and fastened correctly.

" Just curious, if a "full basement foundation" is built on grade, how is it a foundation rather than a first floor/ground floor?" If you can dream it, it can done. My intention was to artificially raise grade, by grading up to the 13' higher second floor, making the second floor appear as a first floor, which would no doubt require thousands of yard of dirt but I had access to free dirt; the size of the lot made it feasible. Visually it would appear as a raised home or on a hill, with a driveway leading up; not an uncommon sight when I lived in NJ. I was keen on a full basement to accommodate a couple of bowling lanes, something I may vaguely consider building as a separate inconspicuous structure somewhere on the lot, however there are other important things at hand now, like completing interior design and renderings; these are close to getting finished, just need to complete designing builtins around the fireplace then the walkin pantry to DW's specific requirements.

@ptreckel I doubt it had radiators. Although it would make sense for the age, I don't see any holes through the original floorboards to the 1st floor that could have been used for the pipes. @Sammy So your telling me that cities had underground oil lines before they had underground natural gas lines? I guess it's possible. There definitely wasn't an outdoor oil tank on site. I remember reading that most homes before the 70s had gas meters inside, but then they were moved outside for some reason.