The game's load times are atrocious even with an SSD. Usually going into a building isn't too bad, but anytime you go from inside a building to outside into the main world the load times are loooooooooooooooooooooooonnnnnnnnnnnnngggggggggg. Often literally measured in minutes instead of seconds.
There are two ways around this (that I know of) and that is to 1) use a mod or 2)run it at extremely high FPS which then breaks the physics (for which a mod is needed). So yeah, basically one way, and that is to use a mod. Now as far as getting things transferred to your SSD, I think your best option probably is to uninstall and reinstall directly to the SSD. But know this, people with extremely fast systems using SSD's still experience long load times. I've got two very good and fast SSD's running in the RAID mode that writes to both simultaneously to make them even faster and vanilla my load times were long enough to sometimes make a sandwich. lol
Now running on an external drive I'm sure makes it worse, and you probably are better off moving it there, just know that this alone won't solve your problem. I'm not sure how you're running the game now (vanilla or modded and at what FPS do you run it at) so I'll just give a little general advice, and also know this... I'm no geek AT ALL and mostly don't know what I'm talking about but I will offer what little I do know.
The major problem with the game that causes such long load times are that it's internal game physics requires the game to be run at no more than 60FPS. Anything over that and the physics start to break, and if you go way over that, well they break even more. Lip syncing becomes way out of whack, you can't jump as high as normal and therefore can't reach normally easily accessible places, as well as some other issues. But at 60FPS, load times become really, really bad.
So there are basically two options (both require mods). One is to use the
High FPS Physics Fix which is an all out mod (thus disabling achievements) and requires the F4SE to use. Note that there are then mods that can re-enable achievements. Allowing the game to run at a very high FPS usually decreases load times immensely. I used to run it at 144 and my load times were much better... but I suffered the physics penalty. I didn't even know it then, and was constantly blaming my controller for not being able to jump to some places I normally would lol. I didn't experience too much lip syncing issues (a few) but I understand that even higher FPS rates lead to even more out of whack lip syncing. Once I learned of the physics issue, i merely changed the refresh rate on my monitor to 60Hz and boom, all of my physics issues were resolved. But then I could go make a sandwich while waiting for it to load whenever I went outside.
So, the second option (my preference since it technically isn't a mod and doesn't change anything else in game like achievements), is to use the
Load Accelerator. To use this one, all you need to do is download the file, unzip it, and place the files that unzip into the directory where Fallout 4 exe is located. One is a DLL file and the other is an ini file to adjust settings. What this mod does is it bypasses the 60FPS limit during loading and vastly decreases load times (the most I see now are just a few seconds). The ini comes initially with a 350 rate set, so I think if your load times are still too slow you might be able to adjust that number higher in the ini file, but I never bothered with it. If you have an FPS counter available, you can see the difference in game. In mine, my game is almost constantly at 60 (a few drops in a few places is all I ever see) but then during loading it jumps up to 350 FPS and makes the loading much, much faster.
However, one caveat with the Load Accelerator, it really only works with SSD's. Some have observed some improvement who use good old HD's, but with SSD's, the difference is stark. And again, I'm no expert (AT ALL lol) but I think the bet bet is uninstall and reinstall to your SSD. If your worried about losing your saves, then try two things. 1)Go to your Documents/My Games/Fallout4/Saves directory and copy all the files in that directory and place them somewhere (on your desktop is fine) as backups, and 2) when you uninstall, I believe GOG gives you the option when uninstalling to delete or not delete the save games, so just choose to keep your saves. If that goes wrong or that option doesn't appear, you should still be okay as a result of step 1. If you have to, you can then just copy or cut and paste those saves back into your new Documents/My Games/Fallout4/Saves folder.
Either way good luck. It really is a great game. There's a bit of some new content with the next gen update (which by the way did NOT fix the awful load times) so hopefully you will get to enjoy that soon as Bethesda says it is coming to gog "soon" lol.
Sorry for the length and hope it helps.