I'm old school, I started riding bikes before they had all these markings on shifters, etc.,etc. So, if you don't have them, you figure out a way to keep track of where you are. As you are aware crossing over is not good.
I've been riding so long that i'm not sure how I learned to do this or hardly how I do this, but let me give a stab at this.
so, say you have 10 gears in back and it sounds like you have a triple up front. (I'm lucky only two in front so I don't have to keep track of 3); just start thinking in sets of five. If you have gone to your small chain ring, you have most likely changed your rear cassette to a lower gear as well, so think if I'm down here, I have 1-3 (most probably, you could have 5 but this would defeat the whole purpose of this exercise) shifts before I go to another chain ring. Then go to the next ring. If you can been in most gears in back in the middle chain ring - there's a place you don't have to pay much attention and then when you are in your big chain ring the same applies as above. Pretty soon with practice, you will pretty much know what gears you are in or close enough.
My husband every once in a while catches me in a cross over even after 20 years of riding - it usually happens when I'm on a casual ride and I'm blabbing my mouth too much! Oh, well, who's perfect?
Hope this helps, but it is hard to remember how I know this stuff sometimes since it comes natural most of the time now, except of course, when I'm not paying the slightest attention to my bike!