One of the foundational ideas of EC is that the past is present now, all around you, in the form of your feelings and emotions. Although you may not remember specifics, feelings and emotions are the most important aspects of your past experience - and this is what is carried forward from life to life to create your experience now and to be resolved. This is your karma, and as you work on a feeling level, you resolve your karma.
In theory, then, we don't really need to know the specifics about the past in order to work on ourselves. Applying the principles now can be completely effective. You say a 'thought' occurred to you. What's the feeling behind the thought? Something like 'I'm no good.' Take it to a feeling level, and apply the steps to that feeling.
We often need to work more on acceptance. The mind interferes when a negative thought/feeling comes up and becomes judgmental, shameful, etc. Put the mind aside and just be present on a body-feeling level with the feeling as you witness it. Remember the dualistic nature of the mind - there will always be the negative. Don't let it throw you. Our intention is to transcend and integrate, not eliminate the negative.
That said, when I'm working with clients, it's common for past-life flashes to come up, and we always honor these and spend time with them to make the most of the opportunity. These recalls are always highly subjective, and we assume there is validity if a strong feeling is associated, but in the end, we don't know for sure if they are true past life memories, and it doesn't matter.
So, my take would be you've got enough to go on now, and if you really need the 'past life' memory, it will come up guided by the higher self, but you don't need to push for it. However, if you want to, it's easy to play around with it. Enter alpha, bring up the feeling by thinking of associated events, and then consciously create a fantasy to match the feeling. At first, it may be only a product of the mind, but eventually a 'real' past-life memory is likely to appear. Stay in the witness and apply the EC steps.
Always remember that you still need to take responsibility for any past-life experiences - the feelings stimulated then are still coming from the suppressed subconscious.