question on how to remove staircase when re-doing floor

I'm planning a new project to add new flooring to my entryway. I have a L-shaped all oak staircase with oak ballusters going up some stairs. I obviously will need to remove the staircase in order to get the new floor under the staircase and ballusters. My question is what is the easiest way to do this.

The style I have is the top rail has a groove underneath where each ballaster slides into, and I assume was brad nailed in, and then a small 1/8" cover goes into the groove to make it smooth. My understanding is that each balluster is likely attached to the bottom via a lag screw which is where the majority of the strength comes from.

What I am considering is to cut each balluster flush where they attach to the ground, and basically be able to have the entire staircase sitting free. I would then remove the old screw and add a long dowel. I would then install the new floor, slightly lifting the particular balluster as I get to it and ensure a small hole is pre-drilled into the floor to align with the dowel. When all done, I would add wood glue to each dowel and basically slide all ballusters down into their dowel at the same time.

Any thoughts on this? Or is there another method that is usually done in these cases.

Thanks