sent her a picture of a to-go menu of her favorite restaurant (which is like a mile from my house) and asked her playfully of what she would recommend. She answered "depends on what I like". I told her that she'll need to come to the restaurant and help me decide .
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Cute! Considering what she said about not being ready for any romantic relationship, I think your approach was good. Maybe even better than good,
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(I think what I said can be considered coaxing, but I feel if I outright asked her for a date it would feel like I'm pursuing more)
Okay, but don't get too hung up about pursuing. This is not the same situation as you were in with your WW. Inviting her out is not pursuing, unless you won't take "NO" for an answer. What you said to her was great. It sounded playful, which is rather difficult over text messaging. May I ask why you text instead of talking with her over the phone?
If you have another opportunity, and since you took the coaxing route this time... I suggest you don't beat around the bush and just ask her if she'd like to join you for dinner. If she gives some excuse, or should she call at the last minute (like she did previously) then you need to move on. Don't get angry or anything, just move on. The world is full of women.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!
Considering what she said about not being ready for any romantic relationship, I think your approach was good. Maybe even better than good, 