Multiple switching LED drivers on single PCB
17 different switchers might sound like a lot, but it is "just" 24 dB more emissions than having only one. Well designed switcher is easily 30 dB from the EMC limits, so there shouldn't really be a problem. Of course you need to design them well, but it's still not as difficult task as you might think.

Without doing more math, to me the EMC trouble seems easier to solve than the heat trouble you'll have if using linear drivers.