In that spirit, I'm going to assume, for the moment, some good faith on the part of the Sad Puppies -- that many of them really thought there was a bias in how the Hugo voting was run, thought that there were, perhaps, secret or not-so-secret voting cabals on the liberal side of the aisle, thought that conservative / Christian / traditional / military authors were being consistently and deliberately shut out. (I don't think any of those are actually the case, personally, nor have I seen any evidence to substantively support those arguments, but the evident sincerity of some posters makes it clear to me that some did genuinely believe that, and perhaps still do.)
I'm even going to assume for the sake of argument that the Sad Puppies's latest effort to suggest a set of pieces to consider for the Hugos wasn't meant to create a lock-step slate, and that they were surprised, and perhaps even dismayed, to find that so many of their supporters voted the party ticket so obviously, thereby knocking out pieces that they themselves would have supported. That they thought they were facilitating a more open voting process, and did not intend the to reap the bloc voting harvest they did. (Also that they didn't expect that so much of professional SF writerdom and readerdom would disapprove so strongly of their methods.)
With those assumptions provisionally in mind, here is what I would suggest to them, to better accomplish their goals:
a) Change your name. Sad Puppies may have been meant as a tongue-in-cheek joke, and you may have some in-group affection for it, but it is irreversibly tainted with association with the Rabid Puppies and this year's voting bloc effect. Also, it carries no useful content to tell the casual reader outside of these conversations what you stand for. Find a name that means something you can believe in.
b) If you still want to intervene in the Hugos (and frankly, I don't know that I think it's worth your time / effort, given that it has a negligible effect on sales -- mostly, it's about writers' ego / pleasure / sense of recognition / validation, and I say this as someone who would very much like to win a Hugo one day), then rather than presenting five choices in each category, present a long list for each category -- I'd say at least a dozen or two titles each. If your real goal is to encourage reading these authors and their works, then let the readers read, and let them decide which ones are award-worthy.
c) Support the awards that already celebrate the writing you love, and/or create those awards if they don't yet exist. I say this as one of the co-founders of the Carl Brandon Society Awards, as a Tiptree juror, and as director of the Speculative Literature Foundation, which has given out the Fountain Award in the past, and which currently gives out a variety of grants to support different kinds of writers and writing. If you see a gap, do the work to fill it. Here is a comprehensive list of SF awards that currently exist: http://www.sfawardswatch.com/?page_id=3
d) Stop using pejorative acronyms, like SJW (to mean social justice warrior), unless you want the general reading public to dismiss you, assuming you're actually anti-social justice (and therefore pro-racism, pro-sexism, etc.). Maybe it's not clear to you that that's how you're coming across, but seriously, that's how it reads to the general public.
That's what I have so far. I imagine there are more possible suggestions. But I think if you even take these four steps, you'll have a far better chance of achieving your agenda of opening up the genre to publishing and reading and appreciating more traditional / military / etc. SF than you are likely to achieve on your current course.
And I am, by the way, a HUGE Bujold and Heinlein fan, and am primarily writing military space opera myself these days. For what it's worth.