Yeah, I would agree with your statement about meditative 'self-checking'. Non-duality teachings all have a self-inquiry component as far as I can tell, although not all of them offer self-inquiry as a way to do work upon our individual selves. In those cases it seems much more like a practice of ignoring ourselves for the sake of having a spiritual experience. The personal self is made to seem like a nuisance that isn't that important, that it should just be ignored and "gotten beyond". But I think we agree that taking that road will only lead to increased self-harm.
Yeah, the rebounding negativity has puzzled me for a time (and was very uncomfortable). It didn't discourage me from further attempts of increasing positivity altogether, but it has found me asking new questions (like in this thread) before moving forward in the practice of 'self-checking' further, since I have been kind of caught-up in a cycle of familiar, repeating negative thoughts or feelings despite consistent work towards the positive. Swimming in circles...
I found myself in the habit of thinking (wrongly it seems) that just relaxing into my positivity, basking in it for a time via inquiry so to speak, would slowly do some kind of dissolving of the negative side on its own (my own misunderstanding and 'wishful thinking'...) I think the 'basking' has helped loosen things up or dissolve them to some extent, but given my "swimming in circles" experience I knew I was missing something. So to your question "what do you believe you should do?", I believe I should continue work towards the positive, but now with more focus on doing work with the negative things that pop up, instead expecting them to disappear eventually on their own through just repeated relaxing-into my more essential, positive self.
If I'm understanding your question, my strongest motivation is to continue to do less and less harm to myself and others, and to come to better understanding of "god" and "the way god made things". Learning about life, reality, creation and its makeup is fun and has something that feels like deeply-meaningful adventure to me (at least when I'm not suffering from my own wishful-thinking lol)