Hi Richard
Google has recently issued guidelines in relation to posts in return for products. They advise that bloggers should no follow links to the company that has given them a free product in return for a post and they should also disclose any such relationship. Here is a good write up on this - https://searchenginewatch.com/2016/03/11/google-issues-guidelines-on-bloggers-and-links-for-freebies/
Again no follow links are definitely not worthless as you must remember they can be a great source of referral traffic, If you get placed on a blog that has a lot of traffic and a highly engaged audience you can gain a lot of exposure from this in the form of referral traffic, social shares and even other links in some cases. Don't purely think of links value in terms of whether they can directly pass authority and help rankings.
If I were working on your project here are some tactics that I would follow:
I would look at identifying influencers in your niche and start to form a relationship with them. Then I would look to get them to write some relevant content on your site, with the aim of giving it exposure to their audience. This is a tactic that I have always found pays off, as it builds traffic and exposure for your site. Ultimately this will lead to lots of opportunities apart from having some good content created for your site that people will see.
I would also look at what your competition are up to that are ranking top for the keys terms you are after. What is there link profile like? What is the content that is ranking like? And what are the social likes and shares to their site and ranking content. This leads nicely into the skyscrapper technique - http://backlinko.com/skyscraper-technique. I would also then look at going a step further with your analysis and evaluate this content very deeply as Rand speaks about in his excellent White Board Friday last week - https://moz.com/blog/category/whiteboard-friday
When you ask whether blogger outreach is dead I don't believe it is - it all just depends the angle you approach it from. I would look to create my own content that can be placed on their sites rather than the quick win of a free product for review. I would still look to get some product reviews but for the reason I mention above. Again I would also look to entice influencers, which quite often are bloggers, to place content on your site to build the authority of your site.
My final note as why I mentioned above, forgetting blogger outreach I would be creating link worthy content and I would be spending a significant amount of time (at least as long as it took to create if not more) to get it placed in different communities on social networks and other sites remembering this is for exposure and not for links. If you create great content that people want then they will share it and they will link to it - it just takes time and commitment (this is why I highlighted the skyscrapper technique above).
Hope this helps!
Matt