How do I fix colour picker to work across different colour-managed monitors?

Question

Hey everyone!
I'm assuming this problem I'm having stems from having colour-calibrated monitors, but let me know if I'm wrong!
To preface, this is the setup I have:
Windows 7
3 monitors as follows, all have individual colour profiles calibrated using the Spyder 3
Cintiq 12WX
Dell U2410
Dell 2409WFP
Photoshop CS6 - Proofed with Monitor RGB, and tested with colour-managed and non-colour-managed documents
I usually do most of my work on the Cintiq 12WX, but pull the photoshop window to my main monitor to do large previews and some corrections. I noticed that the colour picker wouldn't pick colours consistently depending on the monitor the Photoshop window is on.
Here are some video examples:
This is how the colour picker works on my Dell U2410: http://screencast.com/t/lVevxk5Ihk
This is how it works on my Cintiq 12WX: http://screencast.com/t/tdREx4Xyhw9
Main Question
I know the Cintiq's video capture makes the picture look more saturated than the Dell's, but it actually looks fine physically, which is okay. But notice how the Cintiq's colour picker doesn't pick a matching colour. It was actually happening the opposite way for a while (Dell was off, Cintiq was fine), but it magically swapped while I was trying to figure out what was going on. Anyone know what's going on, and how I might fix it?
Thanks for *any* help!
Semi-related Question regarding Colour Management
Colour management has always been the elephant-in-the-room for me when I first tried to calibrate my monitors with a Spyder colourimeter years ago. My monitors looked great, but Photoshop's colours became unpredictable and I decided to abandon the idea of calibrating my monitors for years until recently. I decided to give it another chance and follow some tutorials and articles in an attempt to keep my colours consistent across Photoshop and web browsers, at least. I've been proofing against monitor colour  and exporting for web without an attached profile to keep pictures looking good on web browsers. However, pictures exported as such will look horrible when uploaded to Facebook. Uploading pictures with an attached colour profile makes it look good on Facebook. This has forced me to export 2 versions of a picture, one with an attached colour profile and one without, each time I want to share it across different platform. Is there no way to fix this issue?
Pictures viewed in Windows Photo Viewer are also off-colour, but I think that's because it's not colour managed... but that's a lesser concern.

Answer 1

I think I've figured out the colour management stuff in the secondary question, but the weird eyedropper issue is still happening. Could just be a quirk from working on things across multiple monitors, but I'm hoping someone might know if this is a bug/artifact.
Going to lay out what I inferred from my experiments regarding colour management in case other noobs like me run into the same frustrations as I did. Feel free to correct me if I'm wrong - the following are all based on observation.
General Explanation
A major source of my problems stem from my erroneous assumption that all browsers will use sRGB when rendering images. Apparently, most popular browsers today are colour-managed, and will use an image's embedded colour profile if it exists, and the monitor's colour profile if it doesn't. This was all well and good before I calibrated my monitors, because the profile attached to them by default were either sRGB or a monitor default that's close to it. While you can never guarantee consistency on other people's monitors, you can catch most cases by embedding a colour profile - even if it is sRGB. This forces colour-managed browsers to use sRGB to render your image, while non-colour-managed browsers will simply default to sRGB. sRGB seems to be the profile used by Windows Photo Viewer too, so images saved in other wider gamut colour spaces will look relatively drab when viewed in WPV versus a colour-managed browser.
Another key to figuring all this out was understanding how Profile Assignment and Conversion work, and the somewhat-related soft-proofing feature. Under Edit, you are given the option to either assign a colour profile to the image, or convert the image to another colour profile. Converting an image to a colour profile will replace the colour profile and perform colour compensations so that the image will look as physically close to the original as possible. Assigning a profile only replaces the colour profile but performs no compensations. The latter is simulated when soft-proofing (View > Proof Colors or ctrl/cmd-Y). I had followed bad advice and made the mistake of setting up my proofing to Monitor Color because this made images edited in Photoshop look identical when the same image is viewed in the browser, which was rendering my images with the Monitor's colour profile, which in turn stemmed from yet another bad advice I got against embedding profiles .  This should formally answer Lundberg's bewilderment over my mention of soft-proofing against Monitor Colour.
Conclusion and Typical Workflow (aka TL;DR)
To begin, these are the settings I use:
Color Settings: I leave it default at North American General Purpose 2, but probably switch from sRGB to AdobeRGB or  ProPhoto RGB so I can play in a wider gamut.
Proof Setup: I don't really care about this anymore because I do not soft-proof (ctrl/cmd-Y) in this new workflow.
Let's assume that I have a bunch of photographs I want to post online. RAWs usually come down in the AdobeRGB colour space - a nice, wide gamut that I'll keep while editing. Once I've made my edits, I save the source PSD to prep for export for web.
To export to web, I first Convert to the sRGB profile by going to Edit > Convert to Profile. I select sRGB as the destination space, and change the Intent to either Perceptual or Relative Colorimetric, depending on what looks best to me. This will convert the image to the sRGB colour space while trying to keep the colours as close to the original as possible, although some shift may occur to compensate for the narrower gamut. Next, go to Save for Web. The settings you'll use:
Embed Color Profile CHECKED
Convert to sRGB UNCHECKED (really doesn't matter since you're already in the sRGB colour space)
and Preview set to Internet Standard RGB (this is of no consequence - but it will give a preview of what the image will look like in the sRGB space)
That's it! While there might be a slight shift in colour when you converted from AdobeRGB to sRGB, everything from then on should stay consistent from Photoshop to the browser
Edit: Of course, if you'd like people to view your photos in glorious wide gamut in their colour-managed browsers, you can skip the conversion to sRGB and keep them in AdobeRGB. When Saving for Web, simply remember to Embed the Color Profile, DO NOT convert to sRGB, and set Preview to "Use Document Profile" to see what the image would look like when drawn with the embedded color profile