Per project is dangerous. Consulting clients will change their minds frequently and you'll want to give them the latitude to do so, which means you simply can't estimate the time needed to complete a project without adding X00% on top to compensate. No one wants to have the "this is out of scope, I'm happy to do it but we need to talk about an amendment..." conversation.
Per hour is not adequate for this type of work; you're delivering a product or service that will increase your client's bottom line, you're not a seat-filler who punches a clock. I charge in the smallest increment of time that I believe I can provide a meaningful impact or deliver a complete solution. When asked for a quote I translate my billing into weeks, as in $X000 per week. Accounting for admin tasks and paperwork, back and forth emails and phone calls, plus showing off the work completed and waiting for approval/notes, a week often seems like not enough time (I can't count the number of times a client asking for a simple font change took literally a week to order and get approval on). There are very rare instances where I know I can accomplish a task in days instead of weeks and if the client asks, I will bill in days instead.
"My rate is $X000 per week and my initial estimate is that this will take XX weeks to complete. I require an up-front retainer of X weeks to get started and I bill every two weeks after. Who should I address the initial invoice to?"
I would typically never reveal this tip, but here it goes: "I bill weekly and my normal rate is $X000. For you I would be happy to reduce that to $X000-20%." The client is told up front that they are getting a discount without having to ask for it and the Discount line item on the invoice(s) very much help in getting that invoice paid faster. The secret is that the rate quoted is always 20% higher than what my ideal number is. I make it rain discounts on everyone.
No one wants to have the rate conversation but I've noticed that clients who don't shy away from that talk or flinch at your rate will not be a problem. Clients who complain that you cost too much will be a problem. Politely suggest you are not a good fit for their project and end the call, you're better off. If you get to the point that your non-flinching clients say yes a little too fast to your rate, increase it. You want a little resistance, but not much. Saying yes too fast means you need to charge more.
And lastly, this is not about what work "costs" or "market rates", this is about what your completed solution is worth to your client and how much it will increase their bottom line. You're playing a different game so stop charging like you're mowing lawns or digging ditches. Charge more.