Is this modal system workable?

I'm currently considering a particular modal system for one of my
languages, but I'm not sure how workable it is.

It's closely tied to the languages system of mood inflections, which are
indicative/subjunctive/imperative. Indicative is used for assertions,
subjunctive for non-assertions (hypothetical statements, expressing
doubt, restating presupposed knowledge), and imperative of course for
direct commands. That much is fairly basic. Modality
(epistemic/evidential, deontic, dynamic) is expressed using modal verbs.
That's also not uncommon.

The part I'm worried about is how the modal verbs work. Instead of
having pairs of modal verbs to express epistemic necessity/probability,
deontic obligation/permission, and dynamic willingness/ability, it has
one modal verb for each category. In other words, both "must" and "may"
are the same word in this language (when showing the probability of a
statement's truth value). Likewise, "must" and "can" are the same word
(when showing others' expectations of the agent's behavior), and "will"
and "can" are also the same (when showing internal ability or
willingness). The difference is shown by a modal inflection on the
lexical verb: an epistemic modal verb[1] with an indicative lexical verb
shows epistemic necessity ("must"), while with a subjunctive lexical
verb it shows epistemic possibility ("may"); a dynamic modal with an
indicative lexical shows willigness ("will"), while with a subjunctive
lexical it shows ability ("can"); etc.

The mood inflection on the modal verb is the mood of the overall
statement, which may be determined by grammar (e.g. when used with verbs
of wishing, hoping, or fearing), or by the speaker's trust in his
evidence (in a simple sentence, an epistemic modal would be indicative
if the speaker trusts his evidence, whether the conclusion drawn is that
the lexical statement is necessarily true or just possibly true, while
it may be subjunctive if the speaker is less sure of his conclusion).
For example, when relaying that "John must be in the park", the modal
would be in the indicative if the conclusion is based on a report from a
reliable source (John telling you beforehand that he'll be in the park
at this time), but in the subjunctive if the source is less reliable
(being told by a few people you don't really know that John will be in
the park at this time). The deontic modal is also found in the
imperative: an imperative deontic with an indicative lexical is a strong
jussive/hortative, and can be translated as English "let"; an imperative
deontic with a subjunctive lexical is a more humble plea, and can be
translated as English "may" (as in "May you be at peace"). I think the
dynamic modal can also be imperative, but I'm not sure what that will
mean, exactly.

I find this system satisfying, since it's neat and tidy and makes
logical sense (must be my inner engineer). But I don't know how possible
it is in a natlang--this is supposed to be a "natural language" in a
fictional setting. I don't want to defy any linguistic universals here.

[1] It's actually a mixed epistemic/evidential system: there are
separate modal verbs for conclusions based on direct sensory evidence;
hearsay or reportage; and general principles, tendencies, obligations,
and known habits.