Post-doc vs. Assistant Professor choice, but neither ideal
It is uncommon for people to move up from a teaching school to an R1 school. It happens, but rarely, and your chances are slim. So this seems like a dead end regarding your goal, though of course teaching can be quite satisfying for a lot of us.
The offer of a postdoc elsewhere at least allows you to continue dreaming about a permanent position at an R1 university. Of course, there is never a guarantee that you will get such a position, whereas the AP offer you have at least offers this certainty.
This seems clearly to favor the postdoc position. Teaching 6 courses per year, likely not just 6 sections of one or two courses, will leave you no time for research in any field. Moreover, if everyone else is doing this then there won't be a lot of research synergy that will help you build up your CV.
On the other hand, working in an R1 institution doing research in any field helps you get papers out the door. And you won't get stuck between fields, though you may need to be flexible when it comes to choosing a field for your first R1 faculty position. But no one is required to stick to any particular specialty once they hold a faculty position. You can move to the field you want, and it may be neither of F1 or F2 when the time comes.
Think long term. The teaching position will likely have you teaching for the long term. The research position will more likely have you doing research for the long term. Both of those can be attractive, but maybe not to the same person. Your call.
Just a guess that it is easier to move "over" from one field to another than it is to move "up" to an R1 from a teaching position.
The additional information added by the OP adds some considerations. One that should be considered is the expected size of each section you need to teach. If it is <=10 then it is quite different than if it is 30+.
Otherwise you need to weigh the scales. Citizenship possibilities might weigh heavily depending on your background.