I've been ice fishing most of my life with my older brother who is 10 years my senior. When I was younger (<10 yrs old, I'm 29 now) I was the dedicated pack mule. I pulled the shanty with all our gear on it along with open top minnow buckets. Needless to say I've spilled the bucket more times than I can remember.
One time we went out with his buddy Paul on a large lake in Michigan during a nice cold winter. There's Paul to my left, my brother to the right, and me the pack mule in the middle. About 20 yards out on the ice a large pressure crack that ran at least 100 yards formed directly between my feet. Since Paul and my brother weren't carrying anything, they took off running in opposite directions and I'm left standing going "OK, thanks guys!" Lol. Loud as all hell too. I didn't budge. They walked back to me and we went on fishing.
A few years ago me and my friend Danny were fishing a shallow (10') spring fed lake that dropped off into a 30' basin. It was -14 degrees that day so ice was forming. Pressure cracks forcefully enough to shake my Shappell WideHouse 5500. Constant pressure cracks for about 15 minutes. Knowing that the lake was spring fed and knowing we were around the springs, we didn't take any chances and went to another lake. I wanted to go back to the basin side but Danny didn't feel comfortable at all (he's newer to ice fishing) and I didn't want to put him through the torment and ruin the experience for him. We were only set up for probably 25 minutes before we left.
Like previously mentioned, you did good by being aware and processing your surroundings. A brisk pace is alright but running would be a last resort for me. My feet hit very hard when I run. Keep calm and pay attention to approachig ice at all times.
Glad to hear you used your brain and thought about being safe. A lot of guys I know and fish with don't ever seem concerned about ice conditions. My son is turning 6 this year and he's yet to come out with me because of the mild winters we've been having (Michigan) and it just isn't worth the risk. I'm hoping this year will change that.