My first daughter had never fallen asleep on her own (nursed to sleep) until 5m old, when I started pu/pd. You say you don't have the time, but if possible, get someone to stay with you for at least 3 days (1 week is better)so that you can devote yourself to pu/pd because it works. The first few days pu/pd took up to an hour or more to get her to sleep. Night wakings took far less time. After those first few days pu/pd only took an average of 15 minutes and by 2 weeks I just had to put her in her bed and she'd fall asleep on her own after a bit. I am a sahm and had no help from anyone (even hubby, just his support), so the only real reason you need someone's help is if you've got other kids or have to get to work.
It is hard to make the time, especially if you have other kids to care for, but it is well-worth it. For me, two weeks of dedication to pu/pd, though exhausting then, translated into peaceful nights ever after... well until my second was born! Even through teething and colds she remains a great sleeper.
Good luck!