Deciding on an approach to treat a room is personal decision as there are many products and DIY options, including old standards and more esoteric approaches. The first step, imo, is to define the issues. A common first step is experimenting with household objections, but the problem with blankets and drapes is that they are usually too thin to have decent bandwidth. That is what you are experiencing with the TV cover.
Room calculators are basically useless outside of helping one understand the basic concepts. I would suggest reading Master Handbook of Acoustics to understand room acoustics. I would also suggest in room acoustic measurements, which is far more powerful and accurate than room calculators, so you actually figure out what is going on.
I ended up consulting Nyal Mellor at Acoustic Frontiers out of San Francisco. My room has significant bass and echo challenges. I wanted to solve all the issues at once as well as installing panels with good aesthetics. That is the benefit of the consultant as the consulting fee was very reasonable and much less than the acoustic panels. I did all the measurements, adjustments and the installation. He solved my bass issues at an hourly rate and then created a document describing and grading different parameters of acoustics and then went on to design a solution. He is very good.