this sounds like a pretty good plan. Some doctors do things different ways but titrating you down or slowly decreasing how much sertraline you have is a good idea to avoid withdrawal or problems and then slowly starting the prozac to make sure that gets into your system at a rate that may result in fewer of the start of side effects is a good plan. These drugs I think work very well but they have trial and error for which is a best fit for someone AND they almost always have some start up side effects called transient side effects. They typically go away once you are at a therapeutic level for a while which is at about 6 to 8 weeks. And they gradually get better as you get used to the drug. This is why slowly increasing the dose helps.
So, I think this is a reasonable plan. However, I do agree that you are at risk for a pretty crummy month. Plan for it and cut yourself some slack. Have some go to things that might help such as journaling (good to get feelings out), exercise (mood lifter), deep breathing exercises (breath in for 4 hold 4 breath out for 4 hold 4 repeat), meditation, yoga, etc. And just give yourself a little TLC. My hope is that this strategy and the prozac will eventually help you get on track with depression. Let us know what you think and how you are doing!
Okay, first, you're not on a very high dose of the Zoloft, so there's that. You might need more for it to work. Second, general practitioners know very little about the meds they prescribe. You should do this with a psychiatrist, and a good one, not just anyone, because they are much more experienced with doing this. Which brings me to your taper -- there is no one taper out there. The taper off a drug is the one that works best for you. If this schedule doesn't appear to work for you when you do it, then tell your doc so he can change it up to suit you. You have to tell him how you're doing so he'll know. I also think this particular GP is better than most, he's using a taper that is frequently used by psychiatrists, and he's also tapering you off before starting the new drug, which is also a safer way to do it because that way you'll know if any side effects are from withdrawal or start-up effects from the Prozac. My own experience and research is that there are no tapers shorter than 6 weeks that anyone recommends, so there is that. But it's a very individual thing. I find that when a drug doesn't work, it's not very hard to stop taking. The longer you've been on it the longer it takes to go off of it. These are additional factors. Be safe, be successful, then move on. Best of luck.