Here's my valuation, which is much much more conservative. I'll explain why later on, but let me give you some values first:

Achieve rewards even faster with a 30% point bonus when choosing points
I very conservatively value Hyatt points at 1.15 cents, which conservatively places a value of $345 on how much I would be willing to pay for the 30,000 point Park Hyatts of the world, which seems reasonable to me. The only difference is that I'm fairly sure that my spend would be much, much lower. I'm estimating that I'm spending around $3000 to complete the challenge. It seems very high I'm sure, but given that I'd be burning points if I didn't pay the cash rate and that points are worth something too, I'm sure (or I hope!) that the actual spend from foregoing other brands and points stays will result in a much lower "pure" cost to achieve Diamond status.

I'm almost 100% sure that after completing the challenge I'll have another 5-10 stays/nights at Hyatts, given my crazy burning of points given all the devaluations this year. At $270 on average per night (since I do a lot of FHR stays), that's an additional 6,095 points. At 1.15 cents, this is worth around $90 to me.

Enjoy the best room available upon arrival, excluding suites
$50, because on FHR rates and/or with other elite statuses which I can acquire and maintain for free also have some sort of an upgrade. I do understand that top-tier status is always better than mid/top-tier status that's essentially given away but I don't value that honestly. Maybe once in a while I'll get an incredible upgrade, but outside of that, I wouldn't value this as more than $50.

Receive exclusive access to the Regency Club or Grand Club lounge featuring complimentary continental breakfast and evening hors d’oeuvres. Enjoy daily complimentary full breakfast in hotels without a club lounge
I'm cheap. So I would value the regency club at fast food (or slightly above that) prices and breakfast prices at starbucks prices for coffee and a pastry, because that's what I would actually pay. If I did a Diamond challenge that would mean 12 nights with at least another ~8 paid stays during the qualification period. Or maybe I wouldn't have any more paid stays but I'd have 8 award stays. In any case, in total this benefit for me is worth $160.

Treat yourself to a suite upgrade at the time of reservation four times annually on eligible paid nights
I actually don't value extra space that much. Maybe it's because I'm young, or I don't have a lot of stuff and I don't need a lot of space, but to me each night in a suite if I had to pay for it would be worth around $15 per night, which might be super low, but that's what I would pay if I was given the option to upgrade at a hotel like the Andaz West Hollywood from a standard room to a suite. At 16 nights, that's worth $240.

Receive a special welcome point bonus or food and beverage amenity during each stay
1,000 points times 10 guaranteed stays (20 nights) at 1.15 cents is worth $115 for me.

Receive a nightly room refresh
Negligible. I place no value on this benefit.

Receive the confirmed bed type at check-in
Negligible. I sleep as well on any bed as long as it is wider than a first class bed and is a real mattress

Stay connected with complimentary in-room Internet access
Negligible. I can get internet from most other chains and I'm sure many non-chain hotels would offer this for free.

Expedite check-in at a dedicated area for elite members
Negligible.

Ensure a room is always available with our 48-hour guarantee
Negligible. I would never pay rack rate for a room and I definitely have no need to.

Extend your stay until 4:00 p.m. with a late check out request
Negligible. AMEX FHR and Virtuoso rates have this as well as elite status from the other loyalty programs.

Book reservations through an exclusive Diamond line
Negligible.