Most experienced IR pilots immediately go to the gauges whenever the vis drops--no delays, and no misguided efforts to maintain visual with the ground. It's the attempt to keep visual cues going that gets most into trouble, along with relying on body cues, none of which are reliable in the soup.
While I think you did the right thing to switch on Otto under your circumstances, it's really important to remember that you may not have an Otto to rely on every time. If there's one item most prone to failure in light aircraft, it's the autopilot--and of course, many aren't equipped with one. So being able to handle inadvertent IMC by hand-flying is critical.
I think I've described this event before here, but it's worth repeating. My first start-to-finish private student was a pretty good "stick" very quickly, but he was also arrogant--thought he was better than he was. We'd completed the mandatory 3 hours of IFR training, and he had handled it extremely well--too well, because he just couldn't fathom how difficult flying in actual IMC could be. It was time to do his long dual cross country, and he wanted to go to Jackson, WY--much longer than necessary, but it was his money, and I like going to Jackson. So we loaded up, his wife in the back seat, heading northwest. But as we passed Riverton, it was obvious that we weren't going to make it VFR, as the vis was rapidly dropping. We had some discussion about the lowered vis and he asked if we couldn't file IFR, but there was no way of getting the 172 up to 14,000', the MEA, or 13,500', the MOCA. So I waited while he cogitated and the vis dropped more, and I was actually a bit surprised when he did a 180 back toward better VMC. I then took the controls, told him to plot a course to Casper, and we flew there for lunch.
At Casper, I filed IFR to get back to Laramie, anticipating that we would puncture a cloud or two on the way home, and we did. Soon after passing over Casper Mountain, we were into in-and-out IMC, where the ground was still occasionally visible and the straight line vis ranged from a mile or so down to nothing. Initially he did well, for all of about 30 seconds, when he banked left and loss a little altitude. I tapped his shoulder and the AI, and he immediately regained control. But soon it happened again, I again got his attention, and again he righted the airplane.
So I called Denver Center for a block altitude, and told the controller that this was a training flight so to expect large deviations of altitude and track. My student couldn't hear my comments, because this was in the dark ages before headsets and intercoms were common.
It was obvious to me that my student's focus was divided between the panel and what he could see out of the lower left edge of the windshield. Soon he started to bank again, and this time I didn't say anything. Within seconds the airplane was in a relatively steep dive, turning to the left--the classic grave yard spiral. I let it go until we were almost turned north and had lost a few hundred feet before saying something like, "you might want to get back on course and altitude." He immediately did an unusual attitude recovery, turned around and climbed back to the altitude--but he was visibly shaken. He asked what had happened, and I told him that he needed to stop looking out the window and concentrate on the gauges.
For the next few minutes, he did well, but he was sweating--and it wasn't hot in the airplane. Finally, he admitted that he was overwhelmed and asked if I would take over, so I did. About 20 minutes out of Laramie, we were in good VMC again, and he took over and finished the flight.
What happened to him, and what happened to you, have the common elements of not immediately getting onto the gauges and staying there. As you develop more experience in actual IMC, you'll find that it's easy to momentarily divert your attention to other things and still maintain the necessary scan of the flight gauges--you'll be able to monitor the engine gauges, the struts and leading edges for ice, the chart for in-flight planning, the approach charts to brief for the approach, etc., without losing control. But that comes with practice, and until then, you must concentrate on scanning the gauges without fixating on any particular gauge.
So keep at it, get the IR, and then fly as often as you can in the system so that it all becomes second nature.
Cary