How to make gingerbread more moist and fluffy?

The biggest issue's your facing is the lack of Gluten which helps trap the air created by the baking powder (Fluffy) and the lack of fat (Moisture). I also sure the sugar would be adding a little extra strength. However the Picture on the original recipe looks dense and dry anyway.

I'm assuming you're not using butter purposely, for much the same reason you're using honey instead of sugar.

Taking these two as a basis and working on the recipe you have provided. I think the following may work for you:

3 cups Gluten Free flour
1 cups Honey (Warmed to around 50°C)
1 Packet Instant Yeast <--Previously Baking Powder
1 teaspoons ground cinnamon
1/2 teaspoons ground cloves
1/2 teaspoons ground nutmeg
2 teaspoon ground ginger <--- Not one
2 eggs <-- Stays at 2 instead of halving. 
1 cups milk (Warmed to around 50°C)
1/2 cup maple syrup (Warmed to around 50°C)
3 tablespoons vegetable oil <-- Increases to 3 instead of 2. 

Modified version of: Tasteofhome.com Gingerbread Loaf

1. Mix the warm Milk, Syrup, Milk, Oil and Yeast and leave to ferment for a while (15-25min)
2. Mix the dry ingredients, sieving to trap some extra air.
3. Beat the eggs until fluffy and pale (This would be easier with a couple of teaspoons of sugar if your willing to add a tiny amount?)
4. Mix beaten egg to yeast mix, then add to dry mix, mixing well preferably with a dough hook if you have one. It's going to be hard to do by hand as it'll be sticky as hell.
5. Add to baking dish(es) and leave to prove for an hour. Then beat it back down and leave a further 40min.
6. Bake as described in the original recipe. May need a little longer.

We're aiming for more of a brioche type dough rather than a soft batter or firm bread dough here so more flour may be needed. The above recipe should work well. The only issue may be trapping the air, if this is the case adding 2tsp of Xanthan gum to the dry ingredients will make it work much better. The texture will be much lighter (Fluffy), the additional Oil and Egg should increase the moisture side of things.

Hope this works well for you :), I see no reason it shouldn't.

First of all, let me be clear that I am no expert on gluten-free cooking. I have worked some with gluten-free flours that are primarily made from rice, but Bob's Red Mill All Purpose Gluten Free Baking Flour has a great reputation. I wouldn't assume that is causing you a problem.

Having said that, there were several things I noticed in the recipe you used:

(1) It didn't include salt - you might want to add like 1/2 tsp. salt.

(2) There was almost no ginger in the gingerbread recipe - for your half recipe, I would have used at least 2 tsp. ground ginger and possibly even some fresh grated ginger.

(3) Substituting 3/4 cup honey for 1 cup sugar would add a little liquid to your batter and a couple extra ounces of overall weight - probably not enough to weigh it down against the baking powder and soda that are in the recipe. I think you chose a solid substitution there.

(4) I think the fat content is woefully inadequate. Fats, at least with wheat flours, will tenderize baked breads by impeding the formation of gluten. I don't know how fats work in conjunction with gluten-free flours, but they provide a sense of moistness in baked wheat flour products and I assume they would have a comparable impact of gluten-free breads. In a comparable wheat flour gingerbread, I would have gone with 8 Tbsp. (1 stick) of melted butter rather than 2 Tbsp. oil. Butter will impart a better flavor, for sure. 2 Tbsp. of oil sounds like something from a pancake recipe, not a quickbread recipe.

(5) I don't think your recipe calls for sufficient flour to support the liquid ingredients in your gingerbread. I would recommend increasing your flour from 2 cups to 2 1/4 - 2 1/3 cups (even 2 1/2 cups wouldn't be outrageous). Using a little bit more flour will probably generate the greatest increase in fluffiness.

(6) Rather than baking the gingerbread in a loaf pan, I would recommend baking it in an 8"x8" or 9"x9" square pan. That much batter in a loaf pan can prove too much for any amount of leavening to handle. Having the batter spread-out over a larger area will make a thinner gingerbread, but one that the leavening can handle. Naturally, in a different pan, you would need to adjust your baking time to like 40 or 50 minutes - you can usually tell when gingerbread is done by seeing that the sides have pulled away from the pan and a toothpick inserted in the middle comes out clean.

I hope that isn't too much response. I wanted to be as clear as possible. Basically, more flour, more butter, more ginger, and more pan would be my recommendation. Hopefully a gluten-free expert can weigh-in to cover any considerations I don't know about.