Thinking some more on this, if you pick a schmitt dual supply level translator like TI SN74LXC1T14, you can experiment with 74AHC1GU04 type unbuffered gates as the oscillator, and even try a ROHM BU4SU69G2 ( a HEF4069 4000 single gate part), which would support 32kHz at a higher bias Vcc, for lower current. HCMOS parts will still draw current, even with Vcc close to 1.2V min of the translator.
Adding a BU4S584G2 4000 schmitt could be worth a try, if you are chasing uA, to see if that Icc is less than the input stage Icc of the SN74LXC1T14 when sine driven.
The Nexperia 74AHC1GU04 data has table values for 32kHz operation.