Carb should be a BVF and should be a 30N 2-5, although a BVF 30N 3-1 will also work - thats what I have on mine.
If you fancy spending around £160 you can get a 30mm Mikuni from Allens Performance that is reputed to be very good.
Indeed they should cruise comfortably and smoothly.
For timing just whip the head off and set the piston to (think it's 3mm BTDC) - or whatever the standard timing is (that's what I use on mine) - if the points gap is out that will also make it run badly so check the gap.
Once you have the BTDC setting check that the points are opening at that point and you have it set.
I made some marks with white paint on mine on the rotor under the points so I can easily check / re set points if needed. I have leccy ignition on mine (an old Sparkrite unit) and that has the luxury of an LED that goes out when the points open so it's easy to set timing. Sorry, having re read your email it looks like you do not have points ign - still easy enough to do you just use a multimeter to check the point at which it fires - I used to have a 301 that had the leccy ignition. Wish I never got rid of it as it never surged and had a lot more bottom end that the 251 - you live and learn.
You will get there in the end.
P.S. If it is an original carb the needle jet and needle may be worn making it run rich on the standard settings, also worth checking fuel height as that can also make it run rich. There is a manual at
https://mzriders.files.wordpress.com/20 ... manual.pdf which is worth looking at and covers most things - quality is a bit poor but still readable.