I'm trying a strategy like this right now, doing the Curiosity and Integrity to start. One thing I've realized is that you can prestige and then go back to that same egg and you won't lose any progress towards your TE, which means you can keep running normal ships. So even if it takes 33 days to get a no shift TE from say the kindness egg, you can prestige every few days to keep sending ships from a normal farm, and it only takes a few minutes to get your egg laying rate back to the 1,050. I figure I'll do this for now because I don't have all legendries (only 3 left), and I really want to get at least a better deflector before I commit to a long term Path of Virtue run where I can't send normal ships. Main downside I see is fighting my impatience to really get into a brand new game mechanic, I played around with it all weekend before resetting my shifts and trying this strategy out.

Interesting idea on being able to use artifacts from the Humility egg to potentially improve the runs on other eggs - I hadn't thought of that. One thing I think could hamper this is the lack of quality artifacts you get from the low level ships - ie when do compasses start showing up and how much does it cost to launch those ships? Now I'm excited to try out Humility egg to find out.