The closest size to a 3.00 is 90/90, 3.50 is 100/90.
These sizes are pretty hard to find now, quite a limited selection of tires list them. The Pirellis do not have a 90/90. The 100/90 will fit on the front but is "out of range" - too wide - for the narrow rim and the profile will be distorted. Basically there will be no way to possibly run to the edge of the tread and the "chicken strips" can not be ground off except by hand. There are lots of people who "break the rule", but be aware that it's against the manufacturers recommendation. I don't think there's any danger with a 100/90-18 on the 1.65" front rim though.
There are almost no 3.50-18 0r 100/90-18 rear tires available. The Avon universal is good for both ends. You can go to a 4.00-18 or 110/90-18 without going far outside the recommendations... but there are still few rears made these days.
Any current tire you can get will be much better than the OEM tires. Rubber technology in particular has advanced hugely since the 1970s. Even most el-cheapo tires available today are superior to the best available road tires from then. The K-81 "trigonic" 4.25-18 used to be a popular tire for these bikes, but the current "classic" Dunlop catalog doesn't show that size.