mudlife450 sounds like you are making progress and I agree it would be good to put some hours on it as is as long as you do not have knocking in the lower end.
We picked up a couple of the 325 Magnums and have a lot to learn. If opening the breather box makes it run better the lid intake duct may have insect, etc nest in it like a dirt dauber perhaps so I would run with it off in clean places if the filter is intact as in no holes until you find the air flow restriction.
What kind of oil did you change to before you started it up? More as in what weight?
You may want to change it every couple hours until it says clean if the old oil was dirty.
As I type I see the ZORO tool ad on the right side of the screen promoting Marvel Mystery Oil. I am a Sea Foam addict but for some reason bought some this summer while we were waiting on some parts and replacing all the rubber hoses. Since the oil lines were off (replace them before you ride much because they blow bad) we got some heavy clear plastic tubing and looped from the exit to inlet nipples (we have the Fuji engine) on that one and the other 2002 has the Robin (owned by Fuji) that has a different set up on oil lines.
Warning read with spark Plug REMOVED we dumped in two quarts of marvel Mystery Oil into the crank case with a new oil filter. We put some in the cylinder bore too to soak a few times. About twice a day we would spin it for about 30 seconds with the starter for a few weeks. We did pull the plastic port covers where you adjust the valves to replace them (they get smaller with heat) so we could see MMO was getting to the top of both the intake and exhaust valve train. By the way both of our tappet gaps where .020 when .006 and adjusting them make the top end more quite.
We now have to rebuild the carb that I was hoping we would not because it was loading up and just got worse. We did run it about 20 minutes after the MMO Marvel Mystery Oil and all was well as far as engine sound but it was smoking some but loading up like crazy. I do not suggest to others to do this but MMO is like 5 SAE oil I read.
What I would do with your 325 is with fresh oil and filter I would add either 3 oz of Sea Foam (per label on can) to the crankcase or 8 oz of MMO (20% of oil fill) and run it for an hour or two and check what it looks like on a white paper towel.
One cause of engine smoke (blow by) is the rings, piston and bore are worn out. Another cause is stuck rings (carbon build up) that permit burning of oil and blow by. Sea Foam and MMO were invented to soften carbon build up and they do it quite well for like 75 years now.
Again I would make some rapid oil changes and if I was using Sea Foam or MMO I would just grab some 15W-40 diesel motor oil in your area. Diesel motor oil is very high detergent. Getting your ring grooves and oil path ways cleaned out is important in my mind. Seriously if you will run this for two hours and drain into something clear or like milk jug you will wonder were all the black stuff is coming from. Diesel oil typically as more zinc which is good for our engines.
Even if you are going to rebuild the top end in time you want to de crude the oil flow paths in that 12+ year old engine.
As long as the oil gets black quick I would only ride at low speeds say 30 MPH on the road. The objective is NOT high RPM's when cleaning carbon out of any engine with stuff like SF or MMO but it hours of run time that does the work. I think four 15 minute rides a couple hours apart will remove more carbon than one 1 hour ride.
De carboning a 325 can also help clean the radiator serving as an oil cooler.
Welcome and keep us posted if changing the oil every couple hours helps with the smoking.
If starting with a new filter I would not keep changing the filter each time until I was going to leave the oil in it for a while. They really need synthetic especially if ran hard. If old and ran hard I think changing the oil at 25 hours makes more sense for us that just use them has mules around the farm. I would say riding dusty trails hard for 8 hours might justify an oil change if it does not look like new. I find over time doing short change intervals in an old engine they will start staying cleaner longer because the oil pathways finally become unclogged completely. I learned the hard way dirty oil can cause the oil system by-pass valve to hang open giving little oil pressure in a GM engine.