I am guessing many will say that cheaper imported saddles have this problem,and they're probably right,but have to say I have a one that isn't a cheap import and still have problems with stability,slipping etc,so think TBH it's just a common treeless issue.
Many people on here have been able to solve the problem by using a different pad and shimming etc,so maybe search some threads for ideas on that??
Sorry not more help but as I have exactly the same problem and have not been able to sort it out won't be much help lol
Breastplate could help with the slipping backwards thing,but am guessing you will still have the other issues,so again not much help,sorry!!