If you have a torn-up phillips screw and you cannot get it loose, or need to loosen the security screws on the diaphragm covers,
dannymax suggested a pair of Vise-Grips needlenose pliers. I have an exact same pair, but it just doesn't seem to give me the 'lock' onto the screws that is required, often, the jaws flex, or when I try to put torque on them, they slip-off. I have used a pair of straight-jaw Vise-Grips with success, they seem to give me in my ham-fisted way the correct 'lock' to allow torque to loosen the screws.
"There's more-than one way to 'skin the cat,' and as was mentioned, a good impact driver,
https://www.harborfreight.com/impact-screwdriver-set-with-case-37530.html and good, well-fitting tips is important. Also heed
dannymax's advice, "don't hit that carb body too-hard, or it will fracture!" If you don't have the special bit for the security screw on the diaphragm screw covers (Harbor Freight sells a plastic block holder of security screws) there are several ways to remove it. I often just use the straight-jaw Vise-Grips carefully-positioned, and all it takes is a bit of movement to break them loose.
Another way is to use a hand-held electric grinding tool, like a Dremel or equivalent (Harbor Freight has a 120 volt corded one, cheap
https://www.harborfreight.com/heavy-duty-variable-speed-rotary-tool-kit-31-pc-68696.html ) to simply cut a slot across the head of the security screw, and deep-enough for a slot-head screwdriver to fit tightly into the slot. The screw should then surrender.
The last method would be to use a small cold chisel, and to drive the screw in a proper counter-clockwise direction to release the screw. I've had to do that on all-sorts of screws on a VMax, up-to and including the button-head allen screws which secure the brake rotors, if the allen heads get chewed-up. Any of the other methods I would use before this on a carb screw.
In order of personal preference, I would use the exact security bit (Harbor Freight is one source), the straight-jaw or needle-nose Vise-Grips, then the electric small rotary grinder (Dremel or similar) and finally, the cold chisel. Remember to heed
dannymax's advice about hitting the carb casting! last time I checked, one of the carb bodies wasn't showing up as available on the parts fiche.
Dannymax gives good advice about replacing the screws with allen-head equivalents, just make sure you get the correct thread. Your disassembly will be much quicker next-time. Plus, those round head allen screws look 'cool,' so you've now got that going for you. I like the stainless screws over the black ones as they won't develop rust like the black ones do, especially if the allen head faces 'up,' and collects water. There are tiny buttons you can use to cover the allen head recess if you wish, buy extras, as they like to run for their freedom, when you pry them out to access the allen head for maintenance, and since they're plastic, after being removed a couple of times they can lose their tension, become loose, and fail to stay in-place.
When it's time to replace the set of carbs, if the rubber boots are old and stiff, this may work:
https://www.vmaxforum.net/threads/seat-those-carbs-easily.21303/
As others have posted, some lubricant is an aid in replacing the carbs. Vaseline, K-Y (water-soluble) jelly, WD-40, any suitable lubricant. You don't need much.
Checking for air leaks with some ether or starting fluid, spraying it around the rubber boots, as was-mentioned, once everything is in-place may show you that you need to replace one or more rubber carb donuts. I would recommend doing this every time you remove/replace the carbs, or if you're going to synch the carbs. It's useless to synch the carbs if you have an air leak.
I also am of the "remove the carb cables at the cable junction block" school. If you are having a tough time to get the cables to allow the butterflies to 'snap-closed,' as they should, save yourself the aggravation of looking for problems that aren't there, and go to the cables where they enter the handgrip throttle. See the one that has the screw adjustment with its locknut? Loosen the locknut, and loosen the cable screw to add slack. Now try the throttle. You will probably see that your sticking or slow-to-return throttle now snaps-closed! Just adjust the freeplay for a minimal amount, tighten the locknut, and you should be good to ride.
A tip, if you haven't worked on your carbs before, and you open the junction box to release the cables: the cables run
outside of the frame rails. Be sure that you are connecting the pull cable to the pull cable and the push cable to the push cable. Forget which is which? Just turn the throttle, and watch the cable ends at the junction box. The white plastic cover of the throttle junction box has writing on it to show you where to place the cables.
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