anybody know of a good (and cheap!) water bottle cage that will fit the standard 1liter nalgene bottles?

No one that I know of makes a cage that is designed to fit a regular nalgene bottle, Nalgene does make a 22 0r 24 oz bottle to fit a standard cage. Last summer I ran across a tourist who had spread a Salsa Cage apart to accept a standard Nalgene bottle. I may give it a go myself

My wife uses the type shown below, but there are a few others out there, here is a link to one of them.

That looks like the minoura cage which works great with the PET 1 liter bottles. Awhile back someone else said they tried a 32 oz nalgene in that cage and the bottle was still too wide.

This one from your link looks promising though

Because of the frame size she could not fit 3 smaller bottles so opted for the large 1.5 liter bottle. Good thing about this bottle cage is that it holds the bottle in place by the neck, because of the amount of water it might bounce out.

I had the same problem with my Klean Kanteen which is about the same size as a nalgene. Finally I found this Cannondale bottle cage at REI. I spread out the arms. It holds on tight but allows me to grab the bottle easily.

https://www.topeak.com/2006/products/...dulacagexl.php

This is the same as my wifes, BUT, there is a newer or different model out there that doesn't have the rubberband neck holder, (which quickly wore out and broke on the first tour). The other model has a spring loaded hook that holds the neck of the bottle, but I don't remember were i've seen it. It looked like a much beter design.
She now uses a large/thick plastic tie that fits just over the neck and it works real good, just flip the plastic tie up and pull the bottle.