Anything a person can build, you can unbuild.
+1
I would suggest that your biggest savings would be in the demolition of your old kitchen. Labour is a huge cost in all jobs, and if you can present your hired help with a clean space ready for installation (and maybe even already painted which would save you the aggravation of painting around the cabinets later), you've saved yourself scads of cash right there. You'll also discover ahead of time any previously undetected problems that could hold up the installation, which you could then deal with without having outsiders on the clock. Considering the going labour rate, and you already know how much time it took to take down one cabinet, apply that time figure to the rest of your cabinets x the going hourly rate in your area and you'll see right off the bat how much money you'll save by wrestling those old cabinets out by yourself. Seeing as you're planning on replacing the flooring and countertop anyways along with the cabinets, unless you're planning on reusing them elsewhere, does it really matter if they get damaged during removal? Would your friend be willing to help take your cabinets apart, if not reinstall?
Another option I'm not sure I saw listed here is that if you're not changing the layout of the cabinets, or are simply adding new ones to the existing ones, perhaps refacing the cabinets would be cheaper than reinstalling new ones. If you're happy with your layout you could make a huge visual change with paint and a new door style and hardware, something you could also do yourself.
I've done a kitchen reno similar to what you're describing, and it was done as a mix of DIY and pro help, similar to what you're looking to do, and out of the list you've mentioned, I'd only tackle the baseboards, paint, the tiling, and
maybe the flooring. Gravity is your friend with those four jobs. If you've never tiled before, buy an extra box of tile of the type you're planning to use and practice first; it's not as easy as it looks but 30-60 minutes of 'trial tiling' will tell you immediately if it's something you're willing to take on yourself, and if you're not, you've saved yourself the grief, and the rest of the box is still useable by whomever will do the installation. Same thing with flooring. Snap together laminates or hardwood or engineered can either be really easy or really hard, depending on the flooring chosen, and tools required can range from an exacto knife to a mitre saw to an air nailer. You can rent all of these items, but if you're not comfortable using them, there's an example of how DIY could end up costing more than pro help. Also be aware that your back and knees (and other assorted body parts) will let you know for days exactly how hard the flooring job was.
Most useful tip I ever got (and applied successfully) about kitchen renos: Move your fridge to another room and set up a temporary kitchen - counterspace, dishes and cutlery, a place to sit and eat, a place to wash dishes, etc - and do up a meal plan that involves the stove and oven as little as possible, unless you can move that out too. Bathrooms and laundry rooms work well for this if the counterspace is big enough. If you've always got access to a clean, neat place to eat and prep food, and the space being renovated isn't actually
needed for daily living requirements, the renovation itself will be easier to live with. Your contractor will appreciate it. Your kitchen is going to be a mess each day and if the guys
don't have to spend an hour and a half cleaning up at the end of each day so you can use it to cook, that's an hour and a half more they can actually install stuff, less time to get going each morning, and you're not paying two or three guys $25 an hour (each!) to clean.