The lids are easily removed. They don't need to remain attached.
The insert that comes with the MaxxFan or Fantastic Fan should work for making a box inside the van. It may need some bracing, but at least it is the right size and is made to be cut for the correct depth. That would help with installation.
I'm not afraid to build stuff or try new things, but sometimes there is a product that works better than anything I can make. I had spent a ton of time researching fans, quality, longevity, price, cfm, shrouds, noise, and air exchange only to fall on my face. There are many people who love muffin fans because they work so well for them, but that surely wasn't my experience. Judging by the OP's original comment, she seems to lack the skill to build something that would work well. Nothing wrong with that; we all have our abilities/limitations. However, if she is up to the challenge, using a muffin fan might be right up her alley.
I am in love with my thermostat, so I'm a bigger fan (lol) than most in that regard. I had experimented with a cheap 300 cfm (on max speed) fan shrouded to a window to get an idea how much 300 cfm was and was not satisfied; it usually moved enough air, but sometimes it got pretty chilly by the time I woke up. That doesn't happen now. Mr. Popeil had it right: "Set it and forget it." I want to be comfy not only in temperature, but with my time. I don't want to interrupt my sleep to get up to shut the fan off then go back to bed. When I find myself in hot weather, my trailer needs air flow and lots of it. Having 900 CFM is nice when needed. I'm not a snowbird, so I have more of a need to control my environment. It can be a toasty oat where I live.
You may want to buy a cheap $10 fan like I did that you know what the CFM is, then shroud it to the window. I used cardboard for the shroud; it is an excellent temporary material. Get one with three/four speeds to help you get a better idea of how much air is needed to be moved in your van for your comfort. It will also be noisier, so if you find the noise acceptable, when you do choose a quality fan, you will have an even quieter, stealthier van. Even better, I will offer you my original computer fan as I have no need for it now. It is a high quality one so you would know if a muffin fan will work. Should you accept the fan and it doesn't work for you, forward it to someone who could maybe benefit from it. PM me if you want it. Here is the link to what it is:
https://www.amazon.com/gp/product/B002M78L0A/ref=oh_aui_detailpage_o03_s01?ie=UTF8&psc=1
Space is at a premium in a Caravan. My trailer has ample room for a full sized fan, so space is a non-issue for me.