score:4
Yes why not? Many people do that regularly. There is no problem whatsoever in that plan.
If you had a J1 visa which was going to start its validity after your first trip you could even have gone to Canada for a moment and entered back on the new visa.
There is no such requirement where you have to stay out a specific number of days before reentering on another visa.
Good read: https://iss.washington.edu/procedures/change-status/
See Option 1