The hose that comes off the left side of the engine is the breather. The one that comes off the right side is a return, not a breather; it's supposed to receive oil from the separator thing that you removed, and get it back into the tank. Oil will come out of there; lots of it. You can cork off or plug that hole with no down side.
As for the real breather, back when the design was new it had a duckbill thing that blew any oil that came out (and it's not much) onto the chain. Other bikes and cars just had a road tube or draft tube that dumped whatever came out onto the ground; this will work fine, and contrary to what you might hear, it's a net outflow so it won't suck air and crap back into the engine when it's running (really; trust those of us who remember such things), at least if you have a decent length of tubing; it's crankcase pumping from the piston going up and down (which is potentially an in and out) and ring blowby, which is entirely exhale. If you put your finger over the fitting you'll feel an in-and-out pulsation as the engine breathes, that's why you want some hose length, so it's pulsing essentially clean air and not sucking in. The duckbill is much cooler, however.
If you can find a power steering booster valve or PCV valve with a 3/8 hose fitting on each end, it'll work to make it a one-way exhale, which would be nice and is what the duckbill does as well. So far I haven't found the right part yet.
Route your ONE breather, if you don't go with the duckbill, back over the top of the transmission and down just by the center stand pivot. Alternatively, you can put a short piece of tubing on and put on one of those made-for-the-purpose K&N-looking breather filters, and either fasten it to something, or just let if flop. Running it up to the fender just about guarantees that you'll collect water/oil emulsion condensed from the crankcase vapors, that'll either plug up your hose or drizzle back down into the crankcase, either one of which is not the best idea.
Third choice, get the breather kit our hosts sell, that routes the breather into the oil tank filler.
As for why your valves and piston are not good friends, I suspect that a hard-ish freeway run with only a few hundred miles on the engine could be a contributor; or could you have run out of oil? Respect that it's an antique and take it easy on break-in, for a long, long time.
Which island are you on?