You're right, when things gets tough I use a very clever little end cable that screws into the hose.
I received a pair with a Campagnolo road hydro/groupset and keep them well stored.
You can then pass a shifter cable through it, that stays aligned with the hose.
Drive the cable through the frame.
And pull the hose, even with force.
Does the parktool kit use magnets as well?
That are strong enough?
My initial question was about the handlebar/stem/headset routing.
I'm not sure I look forward to my first time build