I am just writing down thoughts as in many ways it is a open question.
The one component that seems to be absent is social media. Are the blogs being published on twitter, google + facebook etc.? Are the blogs posts topical, educational "the 10 nastiest things we find in your carpet?" etc. Do the customers connect with the blogs.
Given the high bounce rate that means a lack of a strong connection with a customer... a survey - just a simply one of what your customer is missing may uncover some gems - and a path to deepen that connection.
When all else fails ask the customer? Do a site survey.
Site speed is an absolute killer - a study I saw a year ago (cant recall where) states every second over 2 second for page loading you drop 7% of customers. That adds up. Also it is a significant ranking factor.
If I have one priority when I fix a site it is loading speed & usually a tidy up of title, H1's - H4's. Perhaps conduct a site audit - pretend looking at for the first time - be super critical.
So in summary - fix the loading page speed and do some customer research or ask your client to do a customer survey... also everything sounds a little bland.. you need to aim to twice as good as the best... are you doing that?