As I'm kind of out of this project, and not the kind of guy jealously holding informations if it can help, I would like to use this post to give some partial conclusions I ended up by working on the topic.
First key, the one I guess we won't be able to crack soon, even winning this prize, is about genetic code himself. It is very relevant to notice that genetic code makes 21 amino acid with 64 potential combinations of ATGC (3 codons so 4^3). I fear our mathematical models are still not enough evolved to understand really why. I mean if in 3-4,5 Gy of evolution, the genetic code does not exploit all the possibles combinations, there must be some kind of deeper reason than just "nature lacks imagination".
Second key is about geometrical combinations of organic compounds: organic stuff creates c-c boundaries about 109°, and this is not natural tendencies of carbon, this key is somehow related to the need of organic to use some metallic ions like iron or manganese and at the very end, is related to the complex d-layer of transition element, that makes different ionic complexes with compounds like cyanide or ammonia, here is geometrical consideration, but using quantic model that does not fit classical geometry.
You can find a lot of literature (not YouTube stuff, I mean serious papers, go to library or use sci-hub) about ionic complexes and the way it could have been related to the origin of life, in combination with cyanide and ammonia and other stuff (primitive soup hypothesis).
Third key is about not losing yourself too much into theorical considerations and make some try with empirical attitude. But it needs to have a lab available, and this is where I cannot follow my own ideas because it makes a lot of investment for a very thin chance of success, and also require a lot of knowledge about experimental chemistry, long way for maybe nothing at the end, seems like "the research of absolute" ( Flaubert), are we some kind of modern alchemists?
Second key is maybe able to crack for someone with good geometrical skills, I would dig deeper in that direction if I didn't fell like chasing other butterflies, but you won't succeed that direction without going deep into chemical models, mixing with considerations upon redox potentials.
Hope it helped!