My compliments to an artist trying to do engineering. Your work looks good.
"some play in the shaft / bearings". Quantify that. How much play? Can you measure it with calipers?
You must also quantify what is acceptable and what is not. There is no such thing as "no play". You might achieve "no visible play" but there is still some play. Engineers work with numbers. Give us some.
Is this "play" due to imbalance? If so, the best solution is going to be in balancing.
Are you sure this play is actually in the bearings? Are you sure its not in small deflections of the support structure itself? One reason I ask is that the support material appears to be 3D printed, which means plastic. Am I wrong?
I seriously doubt that your situation is severe enough to require heat fitting the bearings. You only see that in high speed, high accuracy spindle assemblies. Not in a 5kg 120 rpm rotating framework.
And yes, all thrust load should be carried by thrust bearings. Depending on their design features, radial bearings cannot generally tolerate significant thrust loads.