Nick, the joke's on me for the second time today. I should have stayed in bed.
I'm often misled by Google, but never (at least until this moment) by LSJ. In translating ἀνάλημμα as "sundial," and κερκίς as "gnomon of a dial," LSJ refers (in both entries) to CIG 2681 (Iasos), which may or may not be the inscription Euterpe is working with.
In any event, of course the two words ought more likely to mean "retaining wall" and "wedge of seats," were it not for ἐπί + genitive in this context. In theatres, the ἀναλήμματα were the retaining walls themselves, not the embankments. Wedges of seats cannot rest upon (ἐπί) the retaining walls, one would think. "Sundial" and "gnomon" seemed to make sense grammatically. Otherwise, we're faced with a textual locus desperatus.
But the blinkin' inscription is, after all, on the wall of a theatre. It finally occurred to me to check ἀνάλημμα in the "addenda et corrigenda" at the back of LSJ (something I almost never bother with), and lo and behold
They've removed any connection between CIG 2681 and the solar analemma, and given the inscription back to the architecture of the theatre! So you're right, Nick, and Euterpe's instincts were correct the words do refer to "something bigger."