I don't mind being so harsh. ;^)
The casimir effect is exciting but it is just 1 of a myriad seemingly unconnected ideas that can be reassembled into various working theories.
I am particularly interested in field theory myself. We don't really understand how force fields work at all. We cannot even explain mass and gravity very adequately.
If you think about it you will realize that a field does not exist in our current dimensions, not really. That part of it which supplies the force to move particles does not have any mass or dimensionality. The region in which it operates (the field) can be defined in 3-d space and time, but what "it" (the force) is and the path it uses for vectoring energy is not understood at all.
Further study of light will be helpful. For the first time we have now actually imaged a light wave, but of course it has mass too...where is that mass when it is an EM wave?
The mathematics we have today is, I believe, very insufficient to explain the next generation of physics.
Newton had to invent new mathematics to help explain his physics (calculus), and other math has come along later, but we need a real revolution in mathematical thinking. we are too bogged down in the complexities, inexactitudes, inelegancies of current mathematics.
Everywhere you turn around a physicist is plugging in a fudge factor or making simplifying assumptions (away from reality).
It is a bit like modelling plasma dynamics in 3-d using slide rules and pencils.
I agree with everything you say.