The community have finally managed to create a simple work-around that should fix the majority of mods that were broken by Bethesda's official v1.5.0.22 (v1.5) patch released on April 28th. I can confirm that this does indeed works. Big props to ElminsterAU and others in the community for creating this solution.

v1.5 is required if you want to run Broken Steel DLC properly. Broken Steel works partially with fan-made alternatives such as "FakePatch v1.5", but the game will usually crash if you have Evil karma and are at Level 21 or higher.

Also FakePatch is based on the ancient v1.0015 patch, which is significantly more unstable than the v1.1 and subsequent patches, especially so for those with Nvidia GPUs.

You'll need the very newest FO3Edit and FOMM (the "Data Files" option in FalloutLauncher.exe isn't up to snuff.)

1. Install and run FOMM and redo your load order. Make sure that Fallout3.esm first, proceeded directly by the ESMs for any DLCs that you have purchased. Once you've done with redoing the load order, close FOMM.

1b. You'll have to move the DLCs from their hidden Windows location to your \Fallout 3\Data\ folder if you haven't already.

This hidden location under Vista is c:\Users\(your windows profile login)\AppData\Local\Microsoft\GFWLive\Downloads\
and for XP it's usually C:\Documents and Settings\(your windows profile login)\Local Settings\Application Data\Microsoft\GFWLive\Downloads\

From there you'll find them within a directories consisting of random characters. Move the ESM file and accompanying two BSA files to \Fallout 3\Data\. For Broken Steel you need to move the accompanying BIK files to \Fallout 3\Data\Video\. Overwriting the older versions of "2 weeks later.bik" and "B09.bik", you may want to rename these as a backup. (Eg B09.bik.old)

To see these hidden folders open a file explorer window and click on Tools Menu -> Folder Options -> "View" tab -> check "Show hidden files and folders".

(Alternatively under Vista you could search for Folder Options from the spotlight search under the Start Menu.)

2. Extract fo3edit.exe + the accompanying essential DAT file to anywhere.

3. Rename fo3edit.exe to fo3masterupdate.exe and run it (this changes the behaviour of FO3Edit entirely).

3a. When patching your mod's ESP files, FO3MasterUpdate may tell you that it's found some errors, look through the generated log file for offending incompatible mods. (Eg Enhanced Blood Textures v1_4a by dDefinder1 wasn't working for me.)

3b. Run FOMM and disable the offending mods by unchecking their ESPs from the load order. Close FOMM.

3c. Run FO3MasterUpdate and once the patching is successful, close it.

You should run FO3MasterUpdate almost every time that you mess around with mods, specifically when you add or remove ones that use ESP plugins.