By implication, trialkoxy would be the most reactive. If borohydride reacted with ethanol, and each product was more reactive, the decomposition should accelerate.
Yes, this has always bothered me. The decomposition should accelerate if each successive species is more basic - this does not always tie well with nucleophilic reactivity though. Despite the inductively withdrawing character of O, there might be overlap between the lone pair and a B-H σ* that encourages hydride donation (but I can't offer a reason as to why this might increase nucleophilicity but not basicity).
It is of course true that trialkoxyaluminium hydrides are less nucleophilically reactive than LAH, which would imply by analogy that (as you propose) reactivity of LiBH
4 decreases with successive reactions with ethanol. Your proposal makes more sense to me.
The question then is why add EtOH to a LiBH
4 reduction?
I have heard of people advocating a "few drops" of alcohol to (they claim) catalyse or activate LiBH
4 reductions - I personally find the reagent capricious at best and avoid it if at all possible.