Lightroom, will do everything that you want it to. You do not need to keep all of the USB drives plugged in at the same time. The only caveat is that you must ensure that each drive always gets assigned the same drive letter. That is actually quite easy to do, at least in Win7and I don't expect that it has got harder in the latest version of Windows. I am still using LR4.4 and as long as LR has already generated the previews for the processed image if one of my external USB drives is off all you get in LR is a little question mark telling you that the file is currently unlocatable. Plug the drive in and LR will simply see the file again (subject to maintaining the drive letter). On my version you cannot do anything to the image if the file is "missing", later versions of LR allow for smart previews, and as long as you have enabled and generated the smart previews you can actually work on a low res preview version of the image while the original file is offline. Although you can also export a very low res version of the image while it is off line, you need to connect the drive to do full size exports and some other functions. All the searching tools, collections and smart collections will still show the image and the keywords etc even when offline. This is even the case for my old version 4.4. I don't know why you think Adobe say you cannot do this. LR doesn't work well with network storage, unless you can have the drive mounted as a drive letter. The issue with networks is that Adobe have not set the database up to deal with multiple users, so you can only have a single user using the lrcat catalogue file. External USB drives though are fine, or I would be in trouble. In the past I even had the catalogue file on a USB2 external drive, although I now have it on the internal SSD.
Alan