You've tried the best two third-party social media scheduling tools that have free options. I don't know that you will find a free alternative that doesn't have some type of restrictions.
How often are you wanting to post? Could you use Buffer in conjunction with Facebook's post scheduler?
That should provide consistent weekly coverage and all for free. If you need to schedule 20+ posts per week, I would upgrade. It's only a few dollars each month and it will probably save you a considerable amount of time if you're going for the volume approach.