This is my plan also. There is no real advantage to going "cold turkey" in fact it probably just really puts a huge load on the lemmy network for no reason as thousands of people are switching so completely in a matter of days. It's great, and it's a great sign for the future of this network, but in a practical sense it just makes it challenging for lemmy to keep up with the traffic and the registrations. Gradual organic growth or even fast growth is a lot easier to manage from a scaling and development point of view than huge sudden spikes like this. It's impressive that the system has scaled as well as it has.
But to focus back on the individual user experience, I think it's fine (and healthy) for your move to lemmy to be gradual. Content is not going to become available overnight, nor should it due to the scaling problems above. If you come here expecting all your huge firehose of reddit content to be replaced instantly, you'll inevitably end up disappointed, and then you'll stop coming here and end up back on reddit full time. Instead, consider this a first step to replace reddit over time, if it's already enough to become your go-to that's great! But if it's not, that's fine too, and you don't have to feel guilty or disappointed about it. Just make the commitment to keep checking occasionally and not forget about it. Add it to your bookmarks, or your homescreen, or your desktop, or wherever it's going to pop up to remind you to check it occasionally. You've planted the seed, give it time to grow into your life.