Ok, lets see,
Reducing the pipe size by 1/4 inch didn't kill your pump. What kills pumps is frequent cycling or severe flow restriction. Ideally you want your off time between cycles to be as long as possible. 5 minutes is great. 1.5 minutes is tolerable as long as it doesn't run this way all the time. Anything below that isn't good for the pump. Also, most pumps are water cooled so you need some flow. If your 50 year old cast iron pipe is corroded inside to the size of 1/4 inch pipe that could be a problem.
Five 1.5 inch 90s and 30 feet of pipe is probably not a deal breaker, but I'm not familiar with battery backup pumps so I don't know for sure. Usually its the height that the pump has to move the water that causes the most drop in flow for sump pumps. If your worried about the number of 1.5 inch 90s just enlarge the pipe to 2 inches and you'll have less resistance to flow at the 90's and over the length of the pipe - problem solved.
Also I'd be concerned about the condition of the iron pipe. It could be corroded to the point that much water is getting through it. If you need to replace it I would run 4 inch PVC under the lawn - assuming you can pitch it so that it will drain by gravity and 2 inch pvc in the house. This will minimize any resistance to flow cause by the pipe.