Why are you losing the fluffiness
Your cake is going stale. The word may surprise you when used here, because people associate "stale" with "old" - but what creates staleness is not time, but physical changes on the microscopic level. And if you freeze a cake, you automatically get these changes.
The main problem is not too-large-ice-crystals, but starch retrogradation. The flour and the cocoa powder in your cake contain raw starch - long polymer molecules tightly packed in granules. When you make your batter, you hydrate the starch (water goes into the granules and binds loosely to the starch) and when you bake it, starch gelatinization occurs - the starch granules burst, and the mixture of free starch molecules and water makes an unordered (=soft) gel. But both starch and water prefer to form ordered, crystalline structures. So starch chains replace their loose bonds to water with slightly stronger bonds to other starch chains, precipitating out of the gel - that is retrogradation.
This process occurs naturally over a few days through brownian motion. But the moment you freeze something, you force it to pack tightly - and give it a very good incentive to get as ordered as it can. So, freezing itself automatically creates an unavoidable, irreversible loss of fluffiness.
This is the main effect you are observing. Other ones can also happen, such as condensation during thawing, or freezer burn, but I don't think they are especially pronounced in your case.
Ideas that won't work
The thought about quick freezing is, at first glance, not so bad. But its main effect is on the size of ice crystals in the water phase, which is important for vegetables or ice cream, but not the main contributor to quality loss in frozen cake. The second problem is that you cannot achieve a quick enough cooling down at home to make a noticeable difference. And third, since you cannot chill it rapidly, you probably plan to keep it chilled at almost 0°C before freezing. Only, I glossed over a ton of information about starch retrogradation in the previous section. One is that starch produces different crystals depending on the conditions under which it retrogrades, and keeping it at fridge temperature produces the hardest, most unpleasant crystals which give the stalest texture.
Making a barrier between the layer and the frosting is also not going to make the cake fluffier. Its problem is that it is losing moisture, not that it is sucking it - and it is using it on a scale where you cannot physically intervene.
What you can do instead
Having established that having the cake stay the same would require you to break the second law of thermodynamics, let's look at ways to cheat.
- Don't freeze the cake
These sculpted mold works are usually made with frosting with some structural stability to it. If you make a smaller cake layer part and thicker frosting, you will probably be able to freeze a thick "shell" out of the frosting and place the cake into it after it comes out of the freezer. I expect that it will need experimentation before it works properly - you probably should freeze a placeholder shaped exactly the cake layer, and then still have some gaps to fill with fresh frosting when combining, which will make your cake somewhat prone to separation. But it feels doable.
Or alternatively, pack the cake bottom with some insulation, and only keep it in the freezer for the minimum of time to get the frosting hard enough to unmold, without having the cake (or most of it) freeze. It will be hard to pull off, but not impossible.
- Do not bake a fluffy cake
If your cake is losing its appeal because it was mostly based on fluffiness, switch to baking a cake whose appeal is not based on being very fluffy. You have different ways to go there. You can try to make your cake more moist and dense, taking it into the direction of brownies. If you want to reengineer the existing recipe to achieve that, some avenues for experimentation would be to stop using almonds, to start using chocolate instead of cocoa powder, to add egg yolks, to increase the amount of fat, to use additives (lecithine and other fatty-teture-imitating ones would be likely candidates) to use a different liquid (cream, sour cream, or apple butter) instead of the rice milk, to reduce the liquid, and to make changes to the sweetener - use more of it, and something with more fructose content than maple syrup, but preferably less moisture (so powdered fructose would be better than corn syrup). As usual when reengineering a cake recipe, don't make more than one change at once, and keep a detailed experiment log for each attempt, or you'll get quite lost.
You can also make a cake that is dry on purpose, going for a genoise or savoiardi style layer or a joconde one (since you are into visuals, you can hide the classic stripes on the inside, that would be fun!). A dacquoise might be an interesting choice, but I don't know how it would react to thawing, especially when embedded in frosting. Or make a recipe which is fluffy when baked, but still tastes good when dried, like some commercial cake bars, because of the very fine, well-dispersed aeration.
- Mask the dryness
You can always syrup your cake. It is a classic technique that not only makes the drying out irrelevant, but also allows you to adjust taste (sweetness) and aroma.
Other options are to make a fine-layered cake, like a Prinzregententorte. Or make the layer out of a cake pop mass or some other form of processed sponge, where you can incorporate moisture and fat.
Conclusion (or TL; DR)
You aren't doing anything wrong. The loss of fluffiness is normal, and unavoidable. As the answers in our general cake-freezing question state, "Different cakes freeze better or worse than others" and "they will not have the same "fresh baked" attributes that a freshly baked cake would", and this is exactly what is happening here. All you can do is to follow the standard cake-freezing advice (wrap it properly, don't let it thaw and freeze repeatedly) which will save you from further problems like freezer burn, but not from loss of fluffiness. If you absolutely insist, you can choose a different recipe where the fluffiness loss is not relevant - but of course that won't be the same cake.