Would this PSNPatch be able to use the data I backed up using ReActPSN to do it?
Yes, both can convert rap to rif (although the implementation details are a little different, and it's not the main feature of PSNPatch)
And I admit, I am not sure what you mean by "activated user".
Any (local - 1st column of xmb) user with a valid act.dat (which officially you can only get via PSN > account > activation > game > activate - or unofficially, for the "aa" user only, by using ReActPSN to install raps)
You see, eboots are encrypted with a key called "Klicensee" which you also need to run them; but since it's only specific to the game, and The Man doesn't want people to "easily" share them, they encrypt the Klicensee itself with a key supplied by the act.dat (which is therefore account specific), and the result is stored into a RIF file - which is the only format a regular console will load them from; so some ingenious people invented the RAP format, which is used to backup/share licenses regardless of act.dat (however, as a format the PS3 OS doesn't know about, you still need to convert them back to RIF with a homebrew of your choice to actually unlock the software)
(I have bent the facts a bit to make the concept easier to understand: if you just read the above, you would think why use RAP instead of Klicensee directly as the account-independent key, which involves some technicalities I have partially forgotten)
My issue is that I have an old 60GB model PS3 on Rebug, it works, but runs hot and the fan is always kicking into max even if I am just idling on the XMB, I am worried it';s going to die soon. So I got a used slim, installed Rebug on that, and am planning to do a system transfer. That slim was not reformatted and has quite a lot of preinstalled PS3 and PS1 games, many of them games I would like and want to keep. Originally I wanted to see if there was some way I coudl extract those games, format the system, and then reinstall them on my user but that seems like it's pretty difficult to do, so I am just going to keep his user and transfer mine from the old PS3 to the slim.
A reasonable and proven way (but not the fastest or easiest) of backing up your games in a console-independent format (rap + pkg straight from Sony) is found in the NoPayStation google sheets database;
you can also probably just extract the licenses with ReActPSN, copy the actual installations (dev_hdd0/game/*) to the other console, install licenses, and rebuild database in recovery - but I never tried, and you might as well go with the more accurate way
Yes, the XMB is heavy (I actually get less temperature, for a fixed fan speed, in some games I play); replacing the thermal paste both above and under the IHS really helps, though