i feel your pain... i do similar experiments, and the biostats people here suggested mixed effects models (fitlme), although that could've been primarily due to the "unbalanced" nature of various levels in various groups of the hierarchy...
recently they told me that (due to not so many observations while trying to estimate too many terms) i should allow ONLY the intercept to vary randomly (by animal, i.e. each animal gets its own intercept, regardless of genotype or other effects taken into account already, because each animal may have a different "baseline", i.e. the intercept represents the response at zero treatment and?or zero depth and?or zero time...). this was after i "reduced" depth to a categorical variable (dorsal or ventral) so that i wouldn't have to worry about random effects of which depth i was sampling from. i imagine you could do the same with at least your depths...
there's a great youtube video on hierarchical linear models you could search called "HLM II: The General Linear Model and the Linear Mixed Model" from "methods consultants of ann arbor" that goes over how ANOVA and regression are mathematically identical somehow i didn't fully comprehend but it's certainly been useful for understanding mixed models.
the split plot experiment (tomato, soil, etc.) in the fitlme documentation (NOT fitlmematrix, although that may be useful for other reasons to you) might be appropriate for what you're looking for in terms of specifying random effects.
i know it's not much, but fwiw
