I never cared for pole construction because there is no flat point to measure from. It really makes it hard to build when there is no reference point. So if you do not want to buy some dimension lumber, my suggestion would be to square the (3) long ridge pole timbers, but please hear me out before you begin groaning! :-)
You do not need woodworking skills to do this, nor have to have fancy tools, or take a lot of your time. I think you could just square up just the two outside faces that the rafters attach too, but making a 4 or 3 square beam would not be that hard either. Now I say all this with
experience, having done this for my timber framed home. Time wise, I was doing 12 foot, 8x8 beams, four sided in 1-1/2 hours. That equates to 7.6 minutes to make a linear foot of 4 sided square beam. Assuming you would get that rate of production or better (conceivably twice as productive you only square two sides), a full day of squaring up timber work, would get you what you need. Honestly, I think spending 8 hours making a squared ridge pole on at least two sides, will make up a lot of time when you install the rafters to the ridgepole.
Somewhere I have a picture of me doing this, but I have not been able to find it on my computer for years. Still, all I used was a tape measure, crayons, a rafter squares, a short level, a chalkline, a regular ole axe, a hammer, and a chainsaw. I also had two saw horses to put the logs on so I was not bending over.
I started by finding the center of each end of the log. Then measuring 4 inches from each side of that, that made a 8 inch square centerd on the log. Then I did the same thing on the other end. Then I took a chalkline, and using nails to hold the end of it (as I work alone too), I laid out the longitudinal lines on the log.
From there, I used my chainsaw and CAREFULL cut down to the lines on each side of the log. I made these cuts every 8 inches. I found this was the ideal spacing so that a I laid my axe flatways to remove the chunk of slab on the log, it would break without too much pounding with the hammer. Naturally this will leave you with a log that is flat on one side. Now just flip the log over and do the opposing side. This will leave you with a log that has two flat sides. Just keep going for (3) sides, or (4) sides...a square beam if you want. (3) 20 foot beams will give you 60 feet of 8x8 ridgepole. Overkill, but they would be free (save a tiny bit of chainsaw gas and bar oil).
The only real caution is, do not make your chainsaw cuts too deep...just go to the lines.
For beams for my house, the look was too rough for me, so I used a hand electric power plane, and smoothed up the beams. That is not required though.