Maybe make an out feed table and tune up your table saw, then make the TS jointer sled. I think a jointer jig for your router would be more finicky to set up and use.
These are the best countersink bit style I’ve found, very clean results, no chatter or tear out: https://www.amazon.com/Gimiton-Countersink-Deburring-Titanium-Insulation/dp/B078Z5QVXS
I think they look pretty cool!
If you want a tip, try this kind of countersink bits, they give a much cleaner cut.