Ranjit: stream of consciousness:
Cramming just before a lesson doesn't work in any case. If you're a good sight reader (you've told us you're not) then you can sort of wing it but even then not really. I've heard teachers say "My student came in basically sight reading. Obviously they didn't practice all week. There's not much moving forward we can do on the piece this lessons."
So on that front there's the situation causing you to cram last minute. I'm assuming that you're extremely strapped for time and couldn't practise all week. Time optimization? Find a way to make 10 minutes daily highly effective, if that's all you have?
I'm also thinking of the habit and ability to study the score before working on it. I don't mean writing in/knowing chord names, or the RN I IV V7 I deal. What is the overall structure? Making a 2nd copy that you can mark up with coloured pencils. Let's take something predictable: a simpler sonata allegro form: [(introduction)] [exposition with 2 themes] [development] [recapitulation] [(coda)]. The two themes; move to Dominant key and back (for the stereotypical older ones). Swaths of things that repeat or almost repeat: patterns that you can recognize but don't need to take the time to listen to the music or play it through to first suss it out. This can save you time.
The other part of playing is identifying difficult parts, getting at them first, having a strategy. But with all that, you should allow it to gel over a number of days (even if you only have 10 minutes/day) because that's how the brain and nervous system work.
This:
ranjit My piano teacher talked about cramming entire Liszt pieces in 3-4 days, or shorter Liszt pieces like those from his Pilgrimages in hours.
and
ranjit And my teacher expects note perfection and good musicality, which is impossible with my terrible sight reading skills.
Sorry, I don't see much guidance in either of these things. The "cramming" to me can set up unrealistic expectations and even feelings of not being up to snuff compared to this teacher (who I think left a whole lot out). The expectations do not show me any sign of guidance. Are these things that you should actually be aiming for?
(edit: I had no idea I'd end up with bullet points)