Deli rye bread without wheat

To me, deli rye is a wheat based bread that relies on gluten for its structure, so the texture probably won't be the same.

Flavor-wise, out of what I have eaten on that list that list I think barley is the closest to wheat. It does have a high soluble fiber content though -- in my experience it soaks up more water than oats or rye -- so might not work out well for the whole portion of non-rye flour. It has taken a very long time to bake every time I've used it for the majority of flour.

I believe what you are trying to achieve may be possible to get close. It all depends on what you expect of a deli rye. Most "deli" ryes these days are dark colored, high wheat content, rye spice flavored loaves that have all the characteristics (bendability, soft texture,elastic) of wheat. If you mean a heartier type of loaf that has reasonable (for a 100% grain) loaf, some bendability and great flavor, then you are in business with my suggestions. Some very delicious experimentation is called for. 

One caution-your friend needs to know if your efforts of baking in a kitchen and with equipment that processes wheat products is not going to cause a cross-contamination reaction. Also, is whatever grain you would use clean of any contamination during the whole process-growing near or on fields formerly used for wheat growing, harvested with wheat free equipment and milled without cross-contamination with wheat. Welcome to the world of allergic individuals. Your best bet is to use "gluten free" labelling as a guide. That is a regulated label in the US. Not so much a "wheat free" label-tho that can be helpful.

Well, once those hurdles are achieved-let the games begin!

My vote goes to buckwheat. Some of these will deliver what you want but some will be quite dense. There is a variation in buckwheat groats and flour available. I got a wonderful dark brown/purplish color to my loaves with Bob's Red Mill whole buckwheat flour. The other variation is when the groats are "shelled" and the resulting loaf turns a greenish tan.

https://www.thefreshloaf.com/node/71127/community-bake-naturally-fermented-buckwheat-bread

https://www.thefreshloaf.com/node/73155/100-buckwheat-bread

https://www.thefreshloaf.com/node/69229/naturally-fermented-buckwheat-bread-no-starter

And then there is rye. MiniOven was the supreme source,a while ago. Look for any of her posts.

https://www.thefreshloaf.com/node/15736/mini039s-favorite-rye-ratio

https://www.thefreshloaf.com/node/33328/minis-100-dark-rye-chia-recipe-love-104-hydration

I cannot leave out Dabrownman. He had many marvelous recipes. I'll let you comb through them.

https://www.thefreshloaf.com/node/50146/dabrownmans-blog-index

Because of the nature of the grains you need to work with, gluten free baking is actually the specialty you will get the most benefit from. Non-wheat baking relies on a mix of whole grains (brown rice, teff,amaranth,buckwheat,quinoa,rye, oat, and barley), starches (tapioca starch, potato starch, cornstarch, arrowroot powder) and structural ingredients like protein and gums: (egg, cheese, soy, nuts, beans) and gums/gels like xanthan gum, gelatin, psyllium, flax, chia, guar gum, pectin. Different ratios,hydrations and handling produce different crumbs. Most (not all) GF is more of a batter consistency dough-like a lot of high percentage rye.

You are on quite the adventure but a lot of this has already been done. In the last 10 yrs, GF baking has come VERY far so you don't have to re-invent the wheel. Keep posting and asking questions. Search GF here on TFL. A surprising amount of knowledge.

EDIT: GF and wheat free baking was around a LONG time before wheat came on the scene so don't get too complicated. Simple recipes will promote the likelihood of more frequent baking. Just as an FYI, I looked into a 100% rice loaf recently but, despite its simplicity, I was not able to get a reasonable texture. Others were successful. OTOH,  buckwheat came through for a similar recipe and procedure. 

My favorite white sandwich bread recipe was from Red Star Yeast website-Buttermilk Sandwich Bread or Farmhouse Sandwich Bread (it's been a while), I believe. That could be adapted to be rye, I bet.

I've been meaning to experiment with the rye-spelt combo for some time.

Try this yeasted batter bread. For "rye bread" flavor, add some bread spice.

BUCKWHEAT BROWN RICE YEASTED SANDWICH BREAD

Ingredients

• 2 cups warm water (around 110°F/43°C)
• 2 tablespoons honey or sugar
• 1 tablespoon plus 1 teaspoon active dry yeast (or 13g)
• ¼ cup plus 2 tablespoons whole psyllium husks (or 30g)
• 1 large egg, room temperature
• ¼ cup olive oil
• 1 ¼ cups light buckwheat flour (or 200g)
• 1 cup brown rice flour (or 160g)
• 1 teaspoon baking powder
• ½ teaspoon sea salt
• Optional toppings: seeds, oats, etc. 

Instructions

1. Prepare a 9x5 inch loaf pan by spraying it with nonstick spray and lining it with parchment paper.
2. In the bowl of a stand mixer, combine warm water, honey, and yeast, letting it sit for 5-10 minutes until frothy to activate the yeast.
3. Using the paddle attachment, add psyllium husks, egg, and olive oil to the yeast mixture and mix until combined, then let it rest for 5 minutes to form a gel.
4. Add the dry ingredients: buckwheat flour, brown rice flour, baking powder, and salt. Mix until a thick, wet batter is formed.
5. Pour the batter into the prepared pan, smooth the top with wet hands or a spatula, cover, and let it rise in a warm spot for about 45 minutes until nearly doubled in size. (I would never raise a GF batter loaf to double. This batter can go from ready to over-proofed in minutes. Treat it like a rye dough-if bubbles are breaking the surface and it is only halfway risen, it is probably done rising.)
6. Preheat the oven to 350°F (175°C) while the dough is rising. Bake for 45-55 minutes until golden brown and it sounds hollow when tapped.
7. Cool the bread in the pan for 5 minutes, then transfer it to a wire rack to cool completely before slicing to ensure it sets properly. 

This recipe produces a tender and springy sandwich bread that serves as a good non-wheat option.