i'll chime in
re: gas in the tank, just make your best guess at how much is in, and add the appropriate amount of oil, then top off with more gas/oil. as long as your close on your guess nothing to worry about, ski won't care if you run 38 instead of 40. you could always run it close to empty so your only "guessing" on the last 2-3 gallons or so. if your really anal siphon it out and measure but that's overkill IMO.
go to west marine, buy a premix container $6, makies getting the proper ratio a snap if you don't have one I have one within walking distance & shipping is like $3. There are other options out there, but the west marine container is great, very snug tight lid, you can toss it in your storage bin and top off at a marina on a longer ride. I have two of them and it works great I can carry enough oil for a full tank.
I do NOT worry about premix sitting, I just took my yamaha 1300 out yesterday, had 6 gallons of gas that's been there 6 weeks, (i've been riding my other ski lately) added 10 gallons of fresh and didn't think twice, it stirs up nicely on the ride to the ramp. I was actually a little more worried about octane than the mix itself, so I never went over 60mph (avoided WOT), but otherwise I never really worried about it. this might be a concern up north, but with me in FL its year round riding and 6 weeks is about the longest a ski will ever sit. Yamalube is not prone to any issues that I've experienced related to it sitting for a longer time, if you were using something like Klotz I'd agree. However, with that said I generaly try to keep my tank closer to empty, so If I know i'm taking a short ride, I might only put in 3/4 of a tank so its closer to empty at the end of the day.
some people really get anal about premix, add oil to a gas tank, shake it, then dump it in, yada yada, IMO a total waste of time, it will mix very very well on the way to the ramp, (ever been behind one of those trucks with a clear water tank on the back? your fuel tank is sloshing around quite a bit) We've discussed this before and I still think 40 is the right ratio, but I use 32 on the advice of my tuner, but I think its due to my fuel controller setup and mods, and that 40 is right for a stocker, but 2x check on that as well.
I've never really located a good/cheap source for yamalube except to just grab it at the local boat shop, mine has a sale every one in a while, but usually i'm paying around $32 a gallon regular $28 on sale.
again, i'm not THAT familiar with the 1200's but I think there is a relatively inexpensive CAT delete that you can do. Mine came with the CAT deleted so i'm not familiar with the procedure/expense/difficulty. Google might sort that out for you. At least with the 1300's the cat delete was very popular but i'm not sure if it was more of a thing to do with a modded ski vs stock, etc...
your carb'd right ? not injected... ?