Does anyone think that not being able to get a job at the majors with 'only tprop/half tprop' time is a function of the major's current economic situation? In contrast, if there were no pilots available... would this experience be viable and relevant to be a pilot in the majors?

My opinion is that majors are just cherry picking, 'cause they can!

I would say get a job in the king or caravan, as any experience is better than not working at all! Good luck with your job search and with whatever decision you make.