DIY IKEA Lack Rack - Preparing the legs?

We are pulling together the parts to build my daughter her first audio rack on the cheap. Another post here about wooden racks brought to my attention some of you who have built racks from IKEA Lack tables, and I became very interested. I already have experience assembling an IKEA wall cabinet for my vinyl, so know that their composite materials are quite strong.

For the rack, you stack the tables up after cutting the legs to size that become your shelves. I want to spike the bottom of the legs, so that they stack up that way. The issue, is the core of the legs are hollow with inside dimensions of 1.75" x 1.75." Dimensional lumber like a 2"x 2" is only 1.5." My idea was using stock square lengths of turning wood that you can get 1.75" x 1.75.

Should I fill the entire length of the legs with the wood, or just insert a shorter piece into the bottom of the legs for the spikes? One of the benefits that's been said about the IKEA composite materials is low resonance even though it's strong. So, will adding a full length of wood to the core of the legs affect the resonance properties? I can go either way.
Kenny