Working at a "Day Rate" seems like a perfect way to do a log home. You show up for work without concern for materials and a game plan. If a material list is needed you take care of it during the day. You get the materials if needed during the day. This is different from the usual business owner where you plan for work after hours and have materials available to have a full productive day.
A good business plan for Day Rate is payment at the end of every day with no collection issues. No pay for today and this GC is off your schedule for tomorrow.
Day Rate is similar to "skilled employee for hire". The problem is a normal skilled employee doesn't do estimates. If I were doing Day Rate I'd have an agreement that says something like "The Day Rate is $XXX.00 per day. Payment due at the end of the day. Non-payment stops work and work is rescheduled after payment".
If I gave an estimate I'd say something like "This estimate is the best-guess which will change with access, cooperation of trades, availability of materials in a timely fashion, weather (on & on with a long list). In much larger and bold font I'd include "THE DAY RATE APPLIES TO ALL WORK".