In my dojo as in a lot of styles the basic entry is an irimi or irmi tenkan with an atemi to the head of uke while the other hand deflect uke's attacking arm.
This is all well and good, except that, just like other interior entry you always risk running into uke's free hand. Anyone with a good martial foundation will keep the other hand in their front arc ready to protect the face or to counter attack. And the free back leg...
For the irimi version, what we were taught was that entering deep is wrong since as you said you'll run into uke's free hand. Technically, it's not irimi tenkan. It is a "hybrid" step. It's more that you step to the side rather than step deep (irimi). You need to ensure that your feet are side by side when you start stepping. The foot that steps should not extend beyond the line of the front foot.
The thing with this is that when you do your atemi, it is just perfect distance where you can reach uke, but uke can't reach you (by a few cms). If uke (1) can atemi you or (2) you have an overreaching atemi, then you've entered too deep. If you have stepped to the side too much then you cannot reach uke for an atemi. These are the tests IMHO for the proper distance.
Stepping to the side also provides the necessary extension to properly offbalance uke. If you've entered deep, then uke will just pivot around his sphere. You need to extend him outside his sphere.
I've attached Chiba-sensei's vid. Although it's too fast, he steps to the side.
movement with katadori is the same