I will be taking a CCW class for, and in, a state that I currently am not permitted.  
As I understand it, per the Federal Safe Passage law,  I can transport from my home state to the class state, with the handgun unloaded, in a locked case, ammo separate, all not accessible by me while driving. . . allowed stops for gas, food, bodily waste extraction. . .
Class is in the evening, and I was planning on staying overnight, and coming home the following morning.  Is that allowed under safe transport, or do I have to return immediately after the class to my home state?

I'd be more concerned about the laws of states you may be passing through (CA, NY, NJ, MA, DE, MD, etc.)  They don't seem to care about Federal laws and may try to jam you up with their state and local laws if have an incident.

FOPA only works if you are legal to possess the guns in your state of trip origin and the place where you stay (delay yourself - class in your case). Since you say that you aren't permitted to possess them in the class state, no you would not be legally covered to bring them there. And certainly not when you are staying overnight . . . one guy spent 3 yrs in a NJ prison doing that.

FYI--home state is NY, class state is RI.  Of course I have my NY Permit. . .
Class is for the non-resident RI carry permit.  
I have a CT non-resident permit as well.  
Looked at RI statutes. . .this  part----seems to indicate no permit is needed "from home to range. . .". . . or am I missing something?

ETA: also part of this class and requirement for the permit application is to qualify on the "Army L" targets---score at least 195, shooting at 25 yds. . .

I can't speak to  RI laws on legality of staying overnight with the firearm.

You can take the RI qualification test anywhere. There is no requirement for any class, just that an NRA instructor test you and certify as such. When I lived in MA, I certified people for RI. I now live in NH and can certify people for RI. The test, including setup and tear-down won't take an hour. The hardest part is finding someone with an Army-L target. I ended up having to order 50 or 100 of them mail-order some years ago and I still have a ton of them.

LenS: thanks for you reply.  I suspect that a large part of the class is to make sure the individual has some basic proficiency,  instruct one on filling out the application, and how to craft the letter to the local PD to ensure approval.  

Coming from my home state where the local .gov would really rather NOT have to give out permits, I understand the necessity of guiding applicants to avoid pitfalls that are purposely planted in the process to try and trip up applications.  

ETA: yes, I found the "L" targets on amazon.  But they are quite expensive---$43 for a qty of 50.

The application is really relatively straight-forward. Each city/town in RI can and does make up their own additional requirements. Letters should be pretty straight-forward as well, since Bruen.

Those targets are damn heavy and huge. My shipment had them doubled over in a long, large box. The "free" shipping also helps make them expensive, but $1 each is probably on the low side these days.