In my own case I first spent some time going through and identifying which L to deal with and then contacted them to find out how they would handle my sitch. There are L rating sites out there (no external links allowed here) which gave me good insight into who to put on my short list. Don't take the first L you find in the Yellow Pages - check reviews, make sure they have experience in what you are dealing with first. Here in my area there is something called "collaborative law" which is a lower cost option. You may want to see if that is available to you as well. It still ends up in the same place but with (so they say) less stress and cost. I'd suggest starting the research and contact process now and then you can schedule a face-to-face with your short list while you are off. It's what I did.
I ended up going with the one from my short list who was the most prompt in getting back to me because being able to turn around any issues in a timely fashion was important. They were also exclusively a family law practice with experience in both collaborative law and divorce. Most L around my area dabble in a bit of everything. When I met with the L, I was very impressed because she "listened" and seemed to understand that although I may be starting the process that I wanted to avoid a D and agreed on an initial plan that would go stage by stage and allow for W to back out at any time. Having a plan has also helped me a lot because now I feel more in control.
Things ended up not working for me the way I'd planned it. W had been going on yet again about moving out like she had for months but even more so. Then one morning she found the cheque I had written to the L clearing through the bank account and asked what it was. I'd not planned on acting for another week when I'd have more stuff together. Her initial reaction was "good". I then gave her a letter I'd written asking her to reconcile but stating that if she didn't want to or didn't respond in a "reasonable time" then I would go legal to end the marriage. I avoided a specific date myself and seem to have done things in the opposite order to you.
I think that the fact that I obviously had a plan in place made things more "real" for her as perhaps did the phrase "end the marriage" vs "separate". I still have no idea where it's going and I've now waited almost 3 weeks. I've been counselled by people who know W and who I trust to be extra patient and so far it's seemed to be working out as she's been quiet about leaving and seems to be making an effort to reconnect. It could just be my imagination though too.
Since you've given a date you need to stick with it - in some fashion at least even if it just giving her the name of your L and asking for her's and requesting an initial meeting. She doesn't need to know how much or little you've done. It will make things more "real" and let her know that her cake eating days are coming to an end one way or another.
Money wise - I've only paid for an hour's consult but the L says that they'll keep my file active and that if I proceed then they'll need about $2000 to start as a retainer.
Good Luck.
On BD H52, W50 T27, M26 S21, D23 BD-9-Mar-16 D-15-Jan-18 Final-19-Apr-18 I am a storyteller. The story may do you no good. But a story is never for the listener. It is always for the one who tells