Can you expand on the type of projects you would do scoping for free for?
Last year I spent 2 and a bit weeks doing paid scoping, because the client knew where they wanted to get (replace a legacy system), didn't know how it worked, didn't know how their business process was structured. Short of a value-based pitch (which has failed with them in the past) the alternative was a guess.
Afterwards we agreed to go onto build the new system. [ There's a whole 'nother side story as I'd lost money on every project I'd done with them before, so this time opted for time & materials - which sort-of worked, but as their max budget was fixed, as was much of the scope, resulted in considerable stress. Still looking for the lesson to learn. ]
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.
Thinking about it, I have a mental block around not billing. I want to see the balance tick up, hour by hour. Any non-billable time is wasted time. Not being paid = no self-worth = I'm wasting my time & got to try harder.
So billing for value, where I haven't "earned" the money by working for it, or putting in a speculative 2-weeks to scope - I'm fighting myself.
[Corollary: I'm very (too) risk averse]
Do you pre-filter clients at all to ensure they have the budget? I've done scoping work for free, only to learn afterwards that the clients budget was 10% of what it needed to be. Do you just accept that as part of doing business, or is there a way to avoid it?
The question I put to you is, would you rather get good at extracting nickels and dimes from clients of a wide spectrum of quality, or would you rather get good at making sure the clients in your pipeline are mostly all high-quality? Billing for scoping time is a good way to get good at the former, and a good way to stay bad at the latter.