I will stick with the Kallax idea.
Actually Walmart do a copy of the Kallax about $7 cheaper per unit.
Looks near identical to my eyes.
However mine are all Ikea Kallax units......
I have been working on a straight grained douglas fir record rack like the LP Bin in the article except with an extra bottom shelf.
Just got to do the dado cuts.  My house, built in 1900, has Doug fir mouldings.
what ever you pick make sure it can grow as your record collection grows and the capacity of most units is about 1/3 less