Q: Electrical power drops out completely while driving.

2003 Jeep Grand Cherokee Laredo 4.0L 305,000+ miles. On startup in the morning, when I put the car in drive and stepped on the gas, electrical power would sometimes drop out completely, then comes back, then does it again sometimes 5 or 6 times (i.e., RPM's go to zero, gas gauge goes to empty, speedometer goes to zero, engine stops running, etc.). Wiggling the key always resolved the problem but sometimes it took several tries (and sometimes a couple of restarts) to find a "sweet spot". After it resolved it ran fine, but once in a great while it skipped a beat again. Throughout the day when I started it the same thing would happen, but not as bad. I have replaced the ignition switch with a new one from Standard Electrical Product. It greatly improved the situation, but sometimes it still happens. Question is, short of having gotten a defective ignition switch off-the-shelf, is there anything else that might cause this? (Bad relay somewhere, etc.) Thanks.

My car has 305000 miles.
My car has an automatic transmission.