When can I find out the next 68N class? Am I even able to reclass to this MOS due to the ins and outs?

You can request it through reenlistment. There's no way to predict when the next class seats will open, you just keep throwing stuff at the wall until it sticks.
I would definitely have a backup request

68N is not balanced, it’s being deleted as an MOS so you won’t be able to get a class date. 68P is the closest thing to it but even then not so much.

Your best choice is to get with your career counselor and let them know what you are interested in. They will be able to see what all of your options are. Do your homework first though and make sure you meet all the criteria as far as line scores and your PUHLES. My best advice is to have a backup MOS that you are interested in as well. I reenlisted to Reclass back in 2007 and I didn't get a class date until 2009. It's good that you lookwd at the In/Out calls as well. That does play a part and let's you know what MOSs are available and accepting your rank.