I'm just going to keep this simple and give you my perspective, which you can take or leave (feel free to ask more questions):
Spend as much time as you think you need to come up with an educated guess.
Build a proposal that quotes a fixed time for the project, but bill the project T&M. Include in your proposal a provision for overage, pro-rated at a daily rate.
Don't bill for scoping work. If it takes 2 weeks to scope your typical project, and those 2 weeks are dragging your practice down, what I'm hearing is that you should raise your rates on delivery, not that you should try to charge some secondary "discovery" rate for or (god forbid) try to bill at your delivery rate.
Spend as much time as you think you need to come up with an educated guess.
Build a proposal that quotes a fixed time for the project, but bill the project T&M. Include in your proposal a provision for overage, pro-rated at a daily rate.
Don't bill for scoping work. If it takes 2 weeks to scope your typical project, and those 2 weeks are dragging your practice down, what I'm hearing is that you should raise your rates on delivery, not that you should try to charge some secondary "discovery" rate for or (god forbid) try to bill at your delivery rate.