Do you know if you can fill a sonotube in multiple pours? I would add rebar to each section embedding it half the way in the wet pour and leaving the other half of the rebar exposed for the new pour. I'm building what amounts to a two story observatory. The floor of the observatory is 10-feet off the ground and I still need to get the pier above that by about 4 feet.
You can, but to do it right is a pain, so it's if it was me, I'd try to pour it all at once. To do it right, you should let the first pour cure for a few days. Then you need to get access to the top of the concrete to roughen and then clean the surface. Roughen it to make a good bonding surface for the second pour, clean it to make sure there is nothing interfering with the bond between first and second pours. The you need to moisten the top to make sure water isn't wicked out of the wet second pour into the surface of the dry first pour. All that access likely means you'll need to take your forms down and then install a new form for the second pour. It's not the end of the world, but hiring a concrete truck and pouring the whole thing at once might be easier than getting that second set of forms nice and straight and lined up with the first pour and keeping everything plumb.
While I am a math nerd, I am not an engineer and I do not know how to calculate deflections and vibration modes. I tend to just over-engineer and call it good.
So, looking at your design sketch, I cannot see a good reason for having three separate columns. I can understand using them in lieu of an unavailable larger size. But if I was doing that, I would place the three columns in contact with each other and have them welded together. That strikes me as a more rigid option than the independent columns.
Yeah, that is where engineering comes in.
Those three columns welded together will be more rigid that each column acting singly. However, there are benefits in rigidity to having the individual columns separated. Since you've admitted to being a math nerd, the area moment of inertia (one factor in figuring out how stiff something is) of a composite section is dependent on the square of the distance between the composite pieces and the centroid of the composite area. That's at the heart of why I-beams and trusses work: they take the load-bearing part of the material and move it away from the centroid, almost like creating a lever arm to multiply your forces (or resistance to forces).
But where you might run into trouble is if the individual columns deflect, or worse buckle, under the loads applied to the structure. It's not likely to happen with telescope loads (we do balance things, after all), but it could happen. That's why I-beams are braced perpendicular to their axes, and trusses have all that cross bracing between the main members: to stop buckling.
All that to say, the calculations aren't that difficult and the OP could figure out if there's an advantage to using his trefoil design to "simulate" a 12" pier, or simply look for some 6" or 8" pipe which he may find is plenty stiff enough for his L350 (and its properly balanced load). The effects of adding lateral bracing to the trefoil design can also be calculated (adding braces in at the midpoint should double the resonant frequency and will increase the load which can be applied before the columns buckle).