What can I do to further reduce solar heat gain with existing Venetian blinds?
One option that can actually help a lot and can diy done is special window film that is made just for that purpose.  I have no affiliation with this company or its products but it was a first hit in a google search  just to give you an idea of what I am referring to.  It looks like they have some good information on their site. https://www.allwindowfilms.com/products/solar-window-film/reflective-window-film

My experience has been with a 3M product but I can't locate the product name quickly. 3M though charges a premium for their name.  Is it any better or not I can't really say. These types of films do work though. Not as well as a replacement window with low-e color reflective glass multiple panes and inert gas filling.  But that gets a lot more involved.  

UPDATE:  I found 3M's info.  https://www.3m.com/3M/en_US/home-window-solutions-us/solutions/  This is the product I would probably suggest, https://www.3m.com/3M/en_US/company-us/all-3m-products/?N=5002385+8709316+8710037+8710654+8710938+8711017+8721691+3292716663&amp;rt=rud