Sounds like a lot of error-prone, manual effort to avoid finding a decent backup tool. OTOH, I've looked for decent backup tools and know your pain. 
They seem as rare as decent database tools/APIs, and even more inflexible if you don't happen to want to use them exactly as their authors wanted to back things up. The you find a good one and it seems to get taken over by management who run it into the ground (mentioning no product names ).
This "mirrored" rename/move thing (wether realtime or not) is for huge files and folders in the first place. An ever growing collection of data get's a pain in the butt sooner or later, especially with HD and 4k video files now.
Currently a rename/move on some of these files or folders containing video/photo/music related data, yields hours of additional backup-time, since you cannot repeat all the changes manually in the backup-locations. I don't know if many people backup their 5TB+ disks, but I do (it twice) and given a steady 50MB/s transfer speed across your LAN, it takes 26,9 hours to fill/update a 5TB hard disk.
The last full backup I ran took around 16 hours, mainly because of renaming or moving around of data (not adding much new). Watch the timestamps of these log files, backup started at around 1:30 in the morning and ended around 18:00 in the evening, just because it needed to copy all those huge files over again, since they were not renamed in the backup.
Yeah - I started my IT career in Backup/Recovery, though in the enterprise rather than consumer/desktop space. I have a whole other level of hatred and disrespect for desktop backup applications because of the demands I was always used to having to satisfy in the datacenter. Sync-back and all of those other backup apps for home users are things I actually never spent much time developing specific issues with because I dismissed them REALLY fast based on quick perception of just the sort of things you mentioned... grrrr.
I don't think adopting tbones suggestion would be particularly error prone though... in a script, I can make sure the file being renamed in the source does in fact exist in the backups, and can even check to make sure it's got the same date and size and other checks to make sure I'm auto-mirror-renaming the intended things, etc. And outside of that, I already 'prefer' to manage my the syncing of my backup datasets manually 'anyway'. So even without some 'help' such as this sort of thing could provide, I'd still be doing the manual way like I am now.
But I might do some other interesting things as well. The rename dialog isn't hard to call up of course, but I often find myself making the same pattern of renames multiple times for related files just by cursoring down the file list because I don't feel like manually typing in the patterns and such. I might do something with an OnRename() event like detecting if other files in a series exist in teh same folder as somethign I'm INLINE renaming, and then prompt me to approve a similar auto-detected pattern rename for the other files... and other esoteric things.
I like automation - but often prefer there to be some intelligent 'prompts' along with kicking off said automation, and one of the things I REALLY like about how you guys implemented the event handling aspect of the scripting features is that we can do things as normal, and apply some intelligence during and after executing something to modify and customize the outcome. This as opposed to having to manually select an alternate way of doign an action (qualifier key, which some of us are running out of 
, or even yet ANOTHER button on my MANY toolbars). What you've done lends very well to contextual automation... and I think rename, copy and copy conflicts have recently emerged as some areas where we'd like to play ...
Getting back to the OnRename()/OnMove() event-thing.
Over the last weeks I created "FOPTracker", a little filesystem watching framework/tool. It's able to track filesystem changes like create/delete/rename file/folder etc. Special feature #1, it's modular (plugins), you can hook your own logic into it. Special feature #2, it's able to detect move-operations, which is something I have not seen before. It's not magic, FOPTracker simply associates delete and create operations within a small timespan, if file-names are equal, voila, there's the move.
A DO plugin is included, watch filesystem changes in the DO script console or react to them by modifiying the belonging script command. The command will be triggered with all the information required to mirror events to another lister/location on the fly, with the commands and tools DO has to offer. No need to set DOs installation path anywhere, it is auto-detected.
By default, FOPTracker will create powershell-scripts for each tracked location (can be disabled). These scripts look like logfiles, but they run as powershell-scripts as well. When run, they redo and repeat all filesystem activities in the location of choice. I use it to mirror all delete/rename/move operations to my backup locations before the actual backup runs. This saves tons of time after heavy renaming or moving of big files and folders, since these don't need to be deleted from the backup, to be copied to the backup again in a different place a few seconds later.
You can create ms-dos batch log/redo-files as well, just notice that this is not tested as heavy as the powershell logging. The tracker can be run on "non-existing" drives and locations, it will just sit and wait until you mount your drives or path to look at. You can eject/remove the tracked location anytime as well, FOPTracker will pause. You can track multiple locations in parallel with one FOPTracker instance (the powershell memory footprint is huge, so we save some hundreds mb of ram compared to running multiple instances). There are bunch of parameters to finetune the tracking to specific files/folders or exclude specific items by type and size.
Requirements:
- Powershell v3+ (Win7 comes with v2, download: microsoft.com/en-us/downloa ... x?id=34595)
- FOPTracker-ScriptCommand and DOpus v11 (optional)
- Since this is "fresh" software, don't run it on expensive space shuttles
- Admin elevation maybe?
FOPTracker running and waiting for activity.. (you don't need the window opened)
DOpus script console, showing incoming FOPTracker events..
Demonstrational redo/repeat powershell script/logfile..
Download v0.2:
FOPTracker.zip (18.2 KB)
Give it a go, I'm quite happy with it! o)
Uh, this offtopic-post got bigger than I intended, sorry! o)