This is a remix of JMK54's design.

In his design, the gear was to be printed, and then pressed onto a metal collar which the gear in 247 sits on. In 367 the gear is completely plastic, pressed onto a spline on the top end of the vertical shaft. But the teeth count and the sizes were identical, so I re-modelled it to make it more like the original plastic bevel gear. There is a "store bought" version of this, but I made this myself, because why buy plastic gears if you have a 3D printer? :P

(store bought version: https://www.singermachines.co.uk/sewingmachineparts/gears/singer-bevel-gear.html)

I've added a chamfer on the entry of the gear bore to help center the shaft when putting it all together.

Design is optimized for 3D printing, so no supports needed, brim would be advised though (it might topple over without one, depending on how good is your bed adhesion).

I've attached the Fusion 360 file, feel free to modify to your liking (might require changing the bore diameter depending on your printer's tolerance so it fits snugly onto the spline with a bit of force)

As for removing the old gear, mine was disintegrating already, so to not take the entire machine apart, I took a flathead screwdriver, a hammer, and gently broke it into pieces, trying to not scrape any other parts inside. Then, I've removed the lower belt (between the shaft and the hook assembly), and the shaft simply slid out. I've gotten rid of old gear crumbs by using a soft, dry brush, and some compressed air (in my case a bike pump :v)

Then, to put the new gear onto the shaft, I first pressed it onto the shaft using vice grips (nice and slow, it has to be almost perfectly centered and straight so it meshes correctly with the metal gear on the main shaft of the machine; took me 3 attempts, first gear had the bore too small, second one was correct but went in crooked, third one worked like a charm). Then, I hanged the shaft by the printed gear in a vice (laid it so the gear was on top of the jaws), and I gently hammered the shaft out using a stick with a similiar diameter to the shaft. This allowed the gear to slide onto the shaft more easily, yet leaving the indentations from the spline bigger as they would be if I modelled the gear bore larger.
Then, I took all the plastic covers off the machine, and I put the gear in place through the holes in the front of the machine, where the stich lenght selector normally is, set it on it's place, meshed it with the main shaft gear, and then I slid the machine off the table until I could reach the vertical shaft hole from the bottom. I inserted the shaft, making sure that it slid into the chamfered bit of the bore, and then I lifted the entire machine, putting it on the table so it stood on the two left legs, and on the shaft sticking out of the bottom. I've pressed down onto the machine, pressing the shaft into the gear as far as I could by hand, then, when the gear was holding the shaft, so it wasn't falling out anymore, I flipped the machine on its back, to have access to the bottom, and hammered the shaft through a piece of wood until it was flush. Then, I ran the machine without connecting the hook with the shaft first, to see if it fits correctly and if the motor doesn't stall (that's what happened on attempt #2, the gear was crooked and it jammed up against the main shaft gear, thus stalling the motor). When it worked correctly, I lubricated it a little with silicon grease, oiled the machine with vaseline oil, since I had it apart anyway, put the belt back onto the shaft and the hook assembly gear, and put the machine back together. Then I re-timed it, and it works for over a week now, heavy sewing for 3-4hrs a day (mostly military clothes, jeans, some faux leather), no hiccups whatsoever.

Great Singer hook timing tutorial here:
https://www.youtube.com/watch?v=k9Ea_xXsneU

Singer 367 teardown (non-English, sadly, but visually good) here:
https://www.youtube.com/watch?v=5OfTik2cOlA