We can rent the camera body for just under $900 for the shoot.
The Alphatron EVF is about another $325 for the month.
Add a shoulder-mount and an EVF thingy and we're staring down the throat of somewhere around $1500 for a month.
But that doesn't include lenses or batteries. I think we're okay with EF lenses, but our power needs are great. Perhaps two of the Switronix PowerBase batteries. So think somewhere in the $1700 range for 30 days of 4K with global shutter.
§§§Remember folks, we'll be shooting at about a 200 ISO for the entire shoot.
§§§We'll need a decent SSD drive for the camera though. Adorama seems to have the best price. Although Ha! They don't have them in stock. So B&H it is. Think $500.
We will also need a reader. Think another hundred bucks.
So $2300 for a month with the Production 4k.
§§§But wait a minute.
If we were to go with a Blackmagic Ursa, two cards and a reader, and a couple batteries, it would be about $2,000. Now we wouldn't have an EVF with that, but we'd have a variety of taps onboard. The camera is about 20lbs but we don't need a shoulder mount (but for about a hundred bucks we could rent one).
Just to make life more difficult the AJA CION is another camera which is interesting. Although all I can find are PL-mount versions and we don't have access to PL-mount lenses. So there.