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Have you considered going into Webmaster tools and clicking on change of address for the previous domain. This way Google knows what is going on and will focus on the new domain.

You already received a lot of helpful suggestions. Have you ever tried http://www.backlinkwatch.com/ ? I use that sometimes to get an extra opinion. I use Semrush as well and always see a difference from that and webmaster tools and etc..

I recently swapped my domain from www.davescomputers.com to www.computer-help.com .

Originally www.computer-help.com was 301 re-directing to www.davescomputers.com ...however my long term goal is to eventually rebrand my business so I decided to utilize the other domain by swapping the main domain.

Is consistant blogging the best way to get Google to re-index the entire website?

My focus has been quality posts and sharing them with vairus social profiles I created.

You already received a lot of helpful suggestions. Have you ever tried http://www.backlinkwatch.com/ ? I use that sometimes to get an extra opinion. I use Semrush as well and always see a difference from that and webmaster tools and etc..