Lead them away from where they are strong: take their centre.
Tenchi nage was explained to me first as two parts: 1/2 sumi otoshi (corner drop) 1/2 irimi nage (fingers past eyes).
Heaven AND Earth, not Heaven OR Earth.
Also, remember to "stand in between Heaven and Earth" (back straight) when you do it (remaining strong in posture and mind).
I totally agree with the sumi otoshi side for the "chi kokyu" part.
For the "tne kokyu" part, you are certainly not wrong in my opinion, but I prefer to associate this part with the hand that goes near uke's elbow for ikkyo.
The draw in for this on is the interesting part. Set you mental intention threw uke's shoulder of the hand that will eventually go up (the same place I feel center power entering me during when ikkyo is being done on me).
For beginners it is helpful to remember to think elbows in (also for shihonage for that matter).
When you throw, if the resistance is on the higher hand, you want to make sure your hips are not facing the same direction as your "ten kokyu" hand. However, IF the resistance is primarily on the lower hand (the "chi kokyu" hand) I would imagine you didn't slide under them as well as you could have. At this point, a good thing to try it so completely switch the sence and raise that hand and lower your other one and go for the other direction.