I'd say for most of those you could plan on $40 for breakfast and internet $15-20 so yes if it's worth your time and trouble then go for it.
I'm not sure what you get as a Plat though so I might be overstating the benefits of Diamond vs Plat.
Plats do get free internet, so the primary savings would be on breakfast, plus the spa at PHT.
Remember that you also get the suite upgrades which can be applied to at least some of those nine nights. The price differential per night can run into hundreds of dollars, which makes the relatively small cost of going for the challenge very worthwhile.
Alternatively, if the majority of the nine nights span from 1 May to 30 June, you can just sign up and not complete the challenge (saving the $440), since you will get Diamond benefits and suite upgrades for the 60 days anyway.
Do award stays count as valid stays for a Diamond challenge? My impression was that they had to be paid stays. Do I get the suite upgrades the moment I become Platinum, even if it's for a challenge?
I don't think your four nights at PHT will count for the challenge, so be sure you're counting the required nights correctly.
Sorry. To clarify, here are my plans:
May 10-14: Four nights at PH Tokyo
May 27-June 8: 12-night mattress run to gain Platinum in the states
July 10-15: Five nights in Australia at various PH, GH properties
I'm counting only those 12 paid nights on the mattress run as the nights that will earn me Platinum.