If we used the true 4x4 we would have to accept losing ½ an inch of head space under the loft (where our kitchen and bathroom will be) and spending time notching ½ an inch off of the last 3 ½ inches on each end.
In order to save time, and head space, as well as weight (douglas fir is super heavy) we ended up deciding to use cedar 4x4s (which are typical dimensions- 3 1/2x 3 1/2”).
We went ahead and framed the majority of the loft using the attractive, lighter, and less dense cedar. When we were a third of the way framed, Jeff started to regret this decision after looking at a lumber density/strength chart online. This prompted a 2 day halt in production while we waited for a reply to an email we sent to Tumbleweed with our concerns.
The engineering technician from Tumbleweed got back to us and confirmed that cedar is an acceptable substitute. With this information, we pressed on and completed the loft framing.
Having a road worthy house is one of our main priorities so our advice to others would be to consider the density and strength of your loft beams.