Minor correction: 802.3bt added 51W (Type 3) or 71W (Type 4). 60W isn't a standard power level. Some switches support up to 95W per port with PoH.
It seems like a weird thing for TFA to say anyway - my PoE[+] switch was the cheapest 8 port I could get a few years ago on Amazon, and does 30W per port. I don't really understand how you could look into it at all, be willing to attempt the hack, but not use a switch (or injector or whatever) that's capable of powering it under load.
This is a good reference for this: https://www.5gtechnologyworld.com/what-every-engineer-should... which goes into how to calc your total bundle dissipation and whatnot.