My degree was in chemical engineering, with modules in renewable energy, and physics training, so I think I can speak with a bit of authority here.
If what you were envisaging were feasible on a home scale it would already exist and be sold in readily packaged forms. There are good reasons why domestic setups have tended towards either photo-electric, or to passive thermal collecting tubes.
Moving parts makes all engineering substantially more complex, difficult and expensive. Failure modes can vary from catastrophic (parabolic lens sets fire to your house), to annoying (your system is offline for weeks in the middle of winter while you wait for parts and time to repair). Passive systems tend to fail in a more benign way, and less frequently - one solar panel in a set might quit, so your system becomes less efficient.
Giant parabolic mirrors scare the crap out of me. I have seen what a moderately sized fresnel lens can do. An array built of parabolic mirrors and hold be worse. Options range from instant blindness, to deep burns, and setting fire to anything organic that ends up in the firing line. Add in a concentrator that is potentially boiling water, or some kind of molten salt, and we have a whole load more scary things. None of these belong anywhere near a home in my opinion. There is a reason that these solar collector system get build in remote deserts.
If you don’t have a rock solid plan to deal with all these hazards, then worrying about efficiency calculations seems like the wrong path to be on.
I’d really recommend steering your attention to other forms of solar intervention. There are loads of simple yet effective DIY arrangements that, for example, increase solar gain in a property, or pre-warm your water supply to reduce the fossil fuel demand of your domestic hot water.
There are many excellent resources available out there. One of my favourite books is
http://www.withouthotair.com/download.html
It was written by one of my university lecturers, and focuses on the situation in the UK. It is a decade old, but still highly relevant.