I found this first-time round and tried to take it as far as I could. I got onto the second level of the teleporter room and was like ‘Nah, fuck this.’
SPOILER
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the first platform is the only one where it gets stuck. go to the bottom floor, and toss it next to the teleporter, so you can pick it up once you get there. then you can safely drop it in. mid floor platform will allow you to pick it up. it might glitch out ocasioanally, but not always like bottom platform. from the mid floor, you can toss it on to the top floor platform with a jump toss easily. it will always fall over if you try it through the teleport.