The artificial thickeners cannot make the bulk of your ice cream. They are only there to give smooth consistency and reduce ice crystal formation in a combination of ingredients which wouldn't mix well otherwise.
The first thing which strikes me is that your recipe has no fat in it, except the little bit from the almond milk. This is a problem. Maybe a food chemist with access to industrial equipment can create a recipe which mimics a normal ice cream only with the ingredients you listed, but it would be exceedingly difficult for a home cook to get to the right proportions and process, and even then, it will be very finicky working with the stuff. Also, I haven't eaten the brand you describe, but knowing all the low fat ice creams I've had, the result is never as good as the real thing. So the first step would be to add fat. The type is not so important, although some will taste better than others. As you can have almond milk, maybe almond oil will be a good fat to use.
Then calculate the proportions of the ice cream body. McGee gives the ratio for good ice creams at 15% sugar, 10 to 20% fat (says that 17% fat are required for smooth freezing in a home ice cream maker), and 60% water. I suppose that the missing ingredients (to sum these figures to 100%) are solids which are neither fat nor sugar, regular ice cream gets them from the egg, dairy and fruit (or other taste carrying ingredients). He doesn't mention starch, I have never made a specifically starch-based ice cream, but have had good results when the starch just comes into the ice cream from ingredients added for flavor, such as pumpkin, chocolate or peas.
So, for 1 liter ice cream base, you want something like 170 g agave syrup (it is not 100% sugar, but a bit less). 150 g almond oil (or another oil) is probably a good place to start for the fat, the almond milk will contribute a little bit more to get to the those 17%, and besides using emulsifiers smooths the ice cream too. Around 2% starch should be sufficient, if you want to use it at all, that is 20 g tapioca. Add 660 g almond milk and you are up to 1000 ml.
I wouldn't use both guar and xanthan gum. They have a good synergy, which is used for making firm jellies, but an ice cream base should be soft. I would use only one or the other, in a concentration of a little below 1%, so something like 8 g would be my first guess. Just add it on top of the 1000 g above, the ratio of fat, solids and water I cited is not so sensitive as to be thrown off by the small addition.
I would start by cooking up the tapioca in the almond milk like regular starch based pudding. When it is ready and cooled off a bit, I'd add the agave, any aroma extracts you want to use and a pinch of salt. Then carefully add the xanthan while mixing with a blender or an immersion blender (they are better than mixers at emulsification). Once the xanthan has been blended in, add the fat, it will emulsify instead of floating on top. If you are using solid fat (coconut oil, shortening), you should probably melt it first.
Leave the prepared base in an ice water bath for a few hours, or overnight in the fridge, for the gum to bind. Then put through the ice cream maker.
I haven't tried the above, and don't know how much of tweaking it will need to become tasty. My knowledge just tells me that it should be close enough to a good recipe to use as a starting point.
The above is for vanilla ice cream, or to use some other extract in small amounts as the flavoring. I would only start experimenting with other tastes when the base recipe has been brought to a stable version. Then it is important to notice that they will bring in more sugar, water and other solids, and adjust the ratio accordingly.