If I was outlining our time skip it would go something like this.
1.During the day, travel and social with Suizhen, hopefully sparing/training so we can cement her loyalty and get a start on building a combat style. Use Quickening to boost her.
2.During our evening hours Cultivate quickly up to Ego, then Spend our first Brush with Cultivation on a Palantíri type Artifact to boost our capacity to find rare Reagents/Treasures/Dungeons/Teachers/Lich's, and the Heroine, a five fold increase in achieving our goals, both now and in the future.
3.Once we've used the exploit to fashion our artifact, mainline Cultivation, we are shortly going to be in Vane, with access to other Lich's, and their spells, notes, and legacies, and the Ring grants major bonuses in Lich wrangling. Baen's notes were a major boon in learning an ascended Sign, I think we can wait to learn the next one till we've seen what bonuses to further Diagram efforts we can pull out of Vane.
As for thrice great? Hide the Diagram, we don't plan to spend much time in central, so it should be fairly simple to pass through as just one more Cultivator, if a gifted one. Lets not complicate things here, just don't draw attention to it and it is likely to be overlooked.
Both our lackeys can learn our secret as we can not expect to hide it from close observation without crippling ourselves.
If it gets out? We have the Backing of two major clans, and high social to boot, we can ride it out.