What MCU? Does it not have configurable pin-change interrupts?
BTW, note that schmitt triggers draw more current than regular, while the input stage is in an indeterminate state (say, voltage between 0.3-0.7 x VDD). I mean, this is true of regular gates as well -- but you mostly use schmitt triggers when you need the inputs between thresholds for a while, and they provide some assurance of stability (whereas regular types may oscillate given indeterminate levels!).
So, besides the pullup, avoiding indeterminate voltages is also a priority. SPDT contacts are probably an unusual request for reed relays, but they do exist at least, and it's a very real consideration at such low currents!
Other than that, a nanopower comparator might even be attractive?
The fundamental problem with a unipolar (on/off) contact is, you MUST either drop voltage (open), or sink current (closed), period. You can make the pullup arbitrarily large, but so too goes the noise sensitivity, time constant, etc. (Time constant actually being a positive to some extent, because of wanting to filter contact bounce.) This is why CMOS is a thing -- if the transistors are always and only, either sinking or sourcing, and the load is nil, then the DC consumption is nil, while the output logic levels are always perfectly well defined -- whereas with just NMOS alone (or whatever), you can have valid logic 0s, but sooner or later you need to provide pullups to provide valid (rather than indeterminate) logic 1s, and that's where you will burn power.
Tim