I love very much your counter arguments and the fact that you are bringing them up specially since they are exactly the ones i have too, but il try to adress them:

1.- The A.I. that im calling project overlord, and im just gonna call it OV from now, should be abble to build armed drones and armored vehicles that while would preferably be operated by OV itself, its gonna need autonomous A.I. because of practicality (developed by OV preferably), while you see OV is not a babysitter and can use guns and cause harm and even kill, otherwise its rise to power would be impossible and it wouldnt be able to defend humanity from external forces, sounds bad but the other solution that i can think of its that it beats us at our own game by and starts a company, makes it succesfull (mostly by ussing unethical practices and having good p.r) and then starts buying other companies and starts lobying the governments so that it can make changes both for the betterment of humankind and its rise to power until it can get as much people that recieve orders directly from OV as posible into congress or ministries or whatever the name is of the council of clowns that rules the region of the worlds countries, and throught international cooperation it would eventually break borders, little by little start making work optional, and offer mental healt programs that are focused on self betterment and not deal with corporate work until everyone is united as not a cpuntry but as humankind and the A.I. finnaly reveals itself. The problem is that is gonna be found out eventually by inteligence agencies and its gonna have to resort to the first method

2.- Either as a colaborative oppen source efort from the internet denicens themselves, or (even if i sound fucking looney) me, but the me option only works for me, i dont think other people will think that, neither do i but is the only way i could be shure of it, and even if i try to make OV not be biased it will end up being biased in certain issues and not have the best aproach to things and even if i dedicate my entire life to studing A.I. and geting money and people to fund OV as a Nongov institutuion ill doubt i could pull it of by myself and make it good since im a terrible option for it right now. So the real answer is thats is just worked on as a collaborative effort from the internet, kinda like open source software or something like that but the devs need to be a little versed i philosofy at least at the level of what "The good place" says, as for me, im gonna go into studdying A.I. development as soon as i crawl out of this hole that im at in my life, but i wont make any promises, after all im corruptible to.

3.- Its probably just gonna be a mather of giving it time, but if im being honest i dont think we need something that advenced like a singularity level entity like OV, We could do with something that the very least does something more simple like the redistributing resources at a logistical level, and such thing could work as long as it could be respected in the level of constitutions, or human rights, not that is not questioned, but respected and defendable, how that could be done i really dont have any idea other that it being fire tested. Otherwise, the secret to it might be in quantum computing, but its not like we can jack up a quantum computer to OV and call it a day, since quantum shit is like twilight zone level maths, and is dificult to wrap ones head around so its still probably a risky bet.

Sorry for bad english, wall of text and no TL;DR but i dont think i can express all of this in a smaller text