I seemed to have found at least a partial solution. I thought it best not to yank Roxio version 126.96.36.199 out of my system, based on the horror stories I've read about what damage that would cause, so I figured I had to reluctantly work with it somehow. First, I have to preface this by saying that I can't guarantee that this will work for everyone, but in my case, with my HP-100 1000 notebook (XP SP3), so far the results have been positive in recovering at least 100 gigs of hard drive space away from Roxio's hogging back-ups.
So, long story short is as follows:
First, download and install Glary Utilities, it's a free program. The Roxio back-up files are hidden but when you run Glary's Disk Space Analyzer, it will detect them under the folder C: System Rollback Data > Restore > Current. In case it doesn't detect it, go to Explorer > Tools > Folder Options > View and un-checkmark 'Hide protected operating system files' then click OK and run Disk Space Analyzer again, though you might have to exit Glary and start it up again for the Analyzer to detect the folder if it doesn't detect it right after you un-checkmark 'Hide protected operating system files.'
In that 'Current' folder will be a few other numbered subfolders. Click each one until you find the mother lode, being a whole slew of other numbered folders. These would come with sizes and creation dates. In my case, I had about 600 such back-up folders usurping over 100 gigs of hard drive space.
Now you want to delete these folders through Glary's Disk Space Analyzer. Not knowing where to begin, I felt that keeping the first week's worth of folders, which dated back to 2009, and the last week's folders would be a safe bet in not screwing up any needed back-up files, especially if the folders numbered in double-digit gig size, like 10 or 20 GB. I would assume those would have everything and more as back-ups. All other folders dated in between I thought would be safe enough to delete as they would be redundant back-ups.
When you delete, one of a few things will happen. You can only delete one folder at a time, which can be a tedious process, especially if you have hundreds of them to scrap, so patience is in order. Some deletions will go quick, while others will take a couple of minutes. Either the deletion will be successful or a message will pop up that a folder can't be deleted for one reason or another. In that case, it's assumed those folders are needed, at least for the time being. No need to panic if that happens, regardless of what message pops up, because it seems that Roxio is just doing its job.
Instead of deleting all that can be deleted and then deleting them from the recycle bin right afterwards, into which they end up, I thought that before deleting them from the recycle bin, I'd restart my computer to make sure it still worked fine and that none of the folders in the recycle bin were crucial ones that Roxio might be screaming for to have. Basically, I deleted about 30-50 folders at a time, after which I restarted my computer and once it was obvious there was no problem by not having any of those folders, I then deleted them from the recycle bin to reclaim my hard drive space. In every case, my computer restarted fine, and by doing so, it simply told me that I could go ahead and delete the next batch of folders that ended up in the recycle bin. Just keep doing this till Roxio won't let you delete any more folders, after which that's probably as far as you can go in getting rid of useless back-ups and reclaiming hard drive space.
Again, depending on how many such folders you have in your Roxio backup 'Current' folder, this would require patience on your part. I estimate that it took me about two hours to clean out as much as I could, but doing so only at about 15-20 minutes at a time over the last few days. I suppose that's also one way to make sure that everything will still run fine if it's done over a period of a few days. In any case, Roxio continues to create more back-ups, but at least it's manageable now and all one would have to do is stick to a schedule of deleting unnecessary back-ups once every couple of weeks or every month, just so that they don't overbloat your computer's hard drive and you won't have to find yourself spending too much time getting rid of them again.
And that is pretty much it. I wish there was a simpler way to do this, and better yet, a way to safely dump Roxio entirely from my computer, but doing it through Glary's Disk Space Analyzer at least helped make it an easy enough process in an intuitive way and it should do for now, at least until I come across the solution I really want. So, hopefully, this'll help any others with this same problem affecting HP 100-1000. It might work for other models, but I can't vouch for that so be wary and play it safe.