For anyone interested, I'll explain in more detail how I deduce the front corners without looking at the bottom. For the sake of simplicity, I'm going to assume that the cross color is white, but the same concept can be applied to any cross color.
First of all, I can sometimes deduce which corner it is by process of elimination. The idea is to use any information about what you currently see/remember about certain pieces to eliminate the other possibility. This is very useful and easy to do when a lot of F2L is already solved, but can sometimes be used earlier as well.
However, sometimes it's easier to deduce the corners by looking at the color pattern formed by the corner and its adjacent cross edges. In other words, the pattern consists of 4 colors in a row. There are three different cases that I will explain separately.
1. Yellow is visible. In this case, we simply ignore it since knowing which yellow corner it is is completely useless information most of the time.
2. White is visible. In this case, we immediately know it's a corner we care about, and we want to know where it belongs. If there are matching colors with white between, the corner is in its own slot. If there are matching colors next to each other, it's in the adjacent slot with that color instead. If there are opposite colors with white between, the corner is in the diagonally opposite slot. And there's only one possibility left for when there are opposite colors next to each other.
3. No white/yellow is visible. In this case, we simply want to know if it's a yellow corner we can ignore or a white corner we care about. If there are two matching colors, the corner is white if they are next to each other and yellow if they form a checkerboard pattern. If there's only one matching color, it's yellow if they're next to each other and white otherwise. And when there are no matching colors, the corner is white if there are two opposite colors next to each other.
Theoretically, it's even possible to deduce the corners without using any other information than the two visible colors, but I personally find that harder to do. I'm very curious about what other people use though! I'm also grateful for any thoughts/questions etc. about the method I'm using
