Just one recommendation if you have the tools on hand.
Make your own almond milk as an initial phase in the trouble-shooting process. It probably can be done in a standard blender, but if you have a higher-speed unit like a VitaMix or equivalent, that
should do the trick. My standard ratio is ~ 1/4 c slivered almonds (no skin) and maybe a few unsalted raw/roasted cashews if they are on hand with a cup of
water or just
enough to cover the blender blades. Blend well.....in the VitaMix after a 2 minute blend on high, the mix is pretty warm. Then add a second cup of water, a bit of oil (~ 1 Tbsp) of your choice if desired, and a pinch of salt and sweetener....the latter all preference and not required. Blend again for about 30 sec. on medium speed. No need to filter if you are making yogurt. Often, but not always, I will bring the milk to a low boil at this step (naturally thickens the nut milk) and then let cool before mixing-in bacterial cultures.
Next, as you noted, mix with either non-dairy yogurt starter or a capsule of probiotics (Lactobacillus mix). Let sit in favorite container at desired temperature for (in my
experience) several days. When done, if you want a thicker consistency, use a nut-milk filter of your choice....reusable bags/strainers or other such item. I double-up a large
coffee filter, pour the mixture in as it sits in a strainer, then straddle the strainer over a deep bowl and let it drain (loosely covered in the fridge) until I like the texture. Flavor as desired. Hope this may help.....if it does you can repeat with the store bought milk and see if it works.
Edited to ask: Did you put the honey in later or during the bacterial culturing? If during, could the natural antibiotics in honey be killing your Lactobacillus cultures?