From reading your post, here are a few ideas.
This is when Uke has regained balance, but Tori has just finished the release. Mainly when Uke turns outside. I have found that I am in a good position behind Uke, he cannot attack me, but the system seems to stall out.
I don't think uke should regain balance. In my mind, right now, today, I want to play Aikido in a way that keeps uke in a constant state of off-balance. Uke regaining balance, I suspect, is causing the stall you mention. This could be caused by uke not launching a committed first attack, or by failing to re-attack. As tori you can also cause a stall condition, sometimes intentional, sometimes not. With #2 & #4 release series, this may be caused by not keeping your hand elevated sufficiently to cause spine-lock in uke. You may want to experiment with having uke attack and finish the release normally, then elevate your hand and see how this affects uke's balance.
I have found myself wanting to make something happen, break balance or draw them down a line, but it doesn't seem to fit because then I am putting in the energy.
I too want to make things happen from time to time. You are correct that by tori putting energy into the system, he takes a chance on being reversed. However, if you have placed uke in an unstable position you stand a much better chance of being successful. It takes very little energy to start the system moving.
One solution I came up with is to drive the connection moving through my center...
Definitely the smart way to do it. This is
hazumi, which is much more powerful than
ikioi which is driven by muscle rather than movement.
I quess my question is does neutrality happen at faster speeds.
Yes and no.
We first need to start with an understanding of the human body. From a stopped position, a human can achieve a speed of approximately 3 feet per second of travel in one step. If we maintain maai, uke has to launch in order to cover distance and reach us. This distance, and uke's launch, are at about 3 feet per second.
Skilled tori's can intentionally induce a stall by executing a very well-timed balance break on uke, and keeping arms relaxed. As uke, I've been hung on my toes on several occasions, perched so perfectly that I didn't want to breathe for fear of the loss of balance it would create. My partner hung me there, and finally released the tension and allowed me to move, just so he could do it again. He knew where I would have to step because of the disequilibrium in our relationship.
As uke, committing too much energy and/or attacking with too much speed will lead to a fall almost every time.