Since Second World will be used to supply pop boosts for third, fourth, fifth colonies, and maybe more, there's less urgency on maxing its factories. This is why I usually rely on it for all my early tech: once it gets up to half factory capacity, not much sense building many more factories yet when the planet is going to sit on half pop for a long time, focusing on emigrating its fertile growth rate out to all the new colonies. Thus, once it reaches that "tech stage" it usually stays there until third and fourth worlds are built up to where they take over the half-pop emmigration duties and I cut back on research for a brief span so second world finally moves on to maxing itself.
Based on my understanding of your description, this puts me on the road to minor tech improvements much faster than you. If not, then where are you getting resources to research? Would have to be from homeworld, right? So... am I to understand that you build all your colony ships from starting tech? That may not be a bad idea on a small map, since the land grab is more in your face and more urgent, but it's definitely not efficient for a big map. Larger maps benefit from a "big picture" approach that gets you more total systems and covers all areas: colony ships, tech, warships and best pop growth rate. You really can have it all, if you max your initial growth curve.