However, I have made a few attempts, and indeed I made such an attempt tonight, as I actually got enough sleep for a few nights in a row and felt up to giving it a shot. Alas, as has been often been the case, I didn't get very far. I did get a few fragmentary memories and fleeting images, but most were disjointed and I couldn't tell you if they were anything but random neuron firings in my brain. There also seemed to be a certain amount of actual psychosomatic resistance– at once point I started getting the itchies, for instance, and scratching an itch in one place would just make one pop up somewhere else.
I asked myself, in my semi-hypnotic state, "What's happening here? Why is there resistance?" and the only response I got was, "No, just no." So for whatever reason, that gate is closed at the moment. Not even a hint as to why, just a flat shut down.
So I guess whatever part of my psyche is connected to all that reincarnation stuff wants me to let it be and concentrate on my current life for now. Which is fine, it's not like I don't have plenty going on. But it's a little frustrating, because I'm still curious. Once you start digging into the notion that what is "you" consists of something much larger than your current trip around the merry-go-round, there is a strong desire (at least in me) to reconnect with the rest. On the other hand, assuming reincarnation is true, then presumably the memory wipe happens for a reason and I'll understand it better once the current trip is done.
However, I'm going on the record as saying now, that I resent you (me) keeping secrets from my (your) self. And I want to remember that part, on the other side.
All of which said, next time I do an "on topic" meditation , it'll be about things in my current life.
 There are different kinds of meditation. The classic "quiet your mind" meditation is generally considered the most useful and provides the most health benefits (physical and mental). However, there's also "meditating on" something, which is getting into that quiet meditative state and letting your subconscious and semi-conscious brain chew on a problem. You just sorta pose the problem to yourself at the start, like releasing a ball at the top of a hill, and let go. It's quite different from actively thinking about something, but honestly, tends to also be much more effective. 
 See also the "have some pie" scene in Men In Black III.