Hi! I totally get wanting an independent nanny, there's often more flexibility with pricing and you can build a real relationship with someone. From what I've heard, it really helps to ask your confinement lady or close friends if they know anyone reliable, since a lot of the good independent ones work through word-of-mouth rather than formal channels. I've heard some mums rave about their nannies and ask them to come back for subsequent babies, which says a lot!
The thing is, independent does mean you're managing everything yourself, no backup if she's unwell, no agency to sort disputes, so weigh that against the peace of mind an agency gives, even if it costs more. Some mums I know ended up going with smaller confinement businesses that feel more personal than big agencies but still have some structure in place. Really depends on what matters most to you, flexibility, cost, or having that safety net. Worth chatting with your gynae or friends who've recently had babies; they usually have the freshest recommendations!