"As we experience the world we do not have the time, nor are we able, to investigate every phenomenon we encounter in a scientific way. Nobody lives this way"

Hello, my name is Nobody, and I live this way.

Certainly, it isn't cheap. I don't have time to go to bars or other wholly frivolous activities. However, it is well within the realm of the possible. Similarly, it is highly worthwhile.  

Everyone who is truly serious about knowledge or wisdom lives this way. 

I make many extraordinary claims, which are reliably verifiable or replicate on demand. How do I solve the problem of consciousness? Etc etc?

Simple: more experience. More effort (though in my case it doesn't count as work). I "work" much harder than anyone; it is not surprising that I know much more than anyone. Indeed it would be rather embarrassing if I didn't dramatically outperform the dabblers and dilettantes (apparently, basically everyone else).