How does suffixing adjectives with "ass" work out grammatically?

Solution 1:

Yes, it's fine to say annoying-ass art teacher (though I don't advise doing that while she's within earshot). When ass is applied as an intensifier, it combines with its host to form an "amplified" adjective. The OED has your back (so to speak):

ass, n.²
4. As the second element in compounds, forming adjectives with the sense ‘having or displaying the quality designated by the first element to an extreme or undesirable degree’, as broad-ass, snobby-ass, cheap-ass, sorry-ass, stupid-ass, long-ass, etc. Cf. ASSED adj.
_{1. See also BIG-ASS adj., PANSY-ASS adj., poor-ass adj. at POOR adj. and n.¹ Compounds 1c, punk-ass adj. at PUNK n.¹ and adj.² Compounds 2, raggedy-ass adj. at RAGGEDY adj. Compounds.}

Diana Elgersma's fine abstract Serious-ass morphology: The anal emphatic in English notes that:

Mono- and bi-syllabic adjectives are the most frequent bases for the ‘-ass’ affix; however, though marked, tri+-syllabic adjectives are not ungrammatical . . .

So, while an·noy·ing-ass doesn't exactly roll off the tongue, you're good to go.

Further reading:

Ass/F***ing Intensification

Asses and big asses