Hyatt Gold Passport - Help timing Hyatt card application

My wife is preparing to apply for the Hyatt card and a couple others very soon, but I wanted to check with people who've maybe been down this road to get some advice. The purpose for applying for the Hyatt card is twofold... one, she has an upcoming paid stay at the Hyatt Regency in Chicago and a suite upgrade would be great, but the main reason is for the two free nights, which we'd like to use at the Park Hyatt Tokyo next year. Most likely we'll be going in April, but it's not 100% certain yet (still have to figure logistics out). I'll eventually be applying for the card myself as well so we can make it four nights, one of which we'll probably use at the Hyatt Regency in Kyoto instead. We'll also probably transfer some Ultimate Rewards points over to Hyatt to make a total of six nights in the two cities, although that part is less for certain.

The only thing that "needs" to happen for this is to get the Chase Hyatt card, first for my wife soon, then for me in a few months because I applied for a Chase card not that long ago. However, I'd certainly like to make it as nice as possible! I'm currently Platinum status for probably 75 more days from the freebie trial that was floating around via Visa Signature, but I can't get it to work for my wife so she's still just Gold. I was thinking she might be able to apply to do a Diamond Challenge.... she has Hilton Gold and Best Western Diamond, although no stays or anything, just from an internet promo. If I get her in the midst of a Diamond challenge, I'm assuming she can upgrade her paid stay in Chicago and then when we book the Tokyo hotel, we'd just use the free night for a suite. "Using up" the diamond challenge opportunity in this manner would be totally worth it; I don't foresee her ever needing it at some other point. If I understand right, even if she gets Platinum prior to applying for the card through the Visa freebie, that would let her upgrade her paid Chicago stay but in Toyko we'll still be in a standard room.

Does this all seem like the best approach? What's the best-case scenario here, or am I already overshooting (e.g., I won't be able to get a Diamond challenge without stays?)

Thanks!

I don't think she'll be able to get a Diamond challenge based on the Hilton Gold without any stays - Hyatt usually wants to see at least 10 stays in the last year in the program that they are basing the challenge on.

And it doesn't help you don't have any stays with Hyatt as well......
It's not exactly like you are a loyal customer.

Does this all seem like the best approach? What's the best-case scenario here, or am I already overshooting (e.g., I won't be able to get a Diamond challenge without stays?)

I think you are definitely overshooting. Your comped platinum status suggests that you have given Hyatt little or no business (at least recently), and you intend to use a credit card bonus offer to stay on the cheap at expensive hotels. I think hoping for a Diamond challenge so you don't even have to pay for breakfast on these free nights is an unreasonable expectation.