First, a caveat...
I worked with someone that worked on voting machines for years and years and speaks at conferences about the flaws in voting systems; flaws that have nothing to do with voting fraud or manipulation and everything to do with flaws in technology and the people that make the technology. This is a fundamental issue with voting that hardly anyone is aware of. Given that, I'm the last person to defend the integrity of our voting systems.
WRT, the amount of time it takes to tabulate votes, while understanding the lengths that are taken to oversee the tabulation, I'd think people would have MORE trust in the system, the longer it takes. My thinking is that more oversight takes more time.