After driving through and removing the top layer of linoleum, I drilled holes just inside my initial cut and continued to drive the square chisel all the way through the floor, alternately driving and drilling as necessary.
In the basement, my helper bolted a 2x8 block to the bottom of each post. While I kept the posts perfectly plumb with a level, he screwed the blocks to the bottoms of the floor joists.
When finished, I tightened the bolts until the washers slightly compressed the surface of the block.
Next came the ipe boards, which I cut about 1/8 inch short so that they wouldn't bind as they slipped into place. Because I'd cut the channel in the tubing for a friction fit, no mechanical attachment was necessary. I simply slipped the boards into the channels at either end, stacking them on top of one another.
I cut a slot in the center of each board with a biscuit joiner and used a single biscuit to keep the boards aligned with one another. I dry-fit the biscuits without glue so that the boards could be removed and replaced easily in the event of damage.