Plenty of FOSS is dual licensed, this really isn’t as hard or complicated as some are making it out to be.
But your intent, if you want to avoid for-profit organizations using your software, is to impose a restriction on users not to redistribute the software in certain ways. It is your right to add such a restriction to your software, but it is no longer FOSS, since that term necessarily implies an unlimited right to redistribution (within the law).
Redistribution is unlimited for all non-commercial use. This has been through legal review.
If you’re still confused, please contact me directly and I’ll be happy to answer any other questions.