IRS2003 half bridge driver
Your analysis appears to be correct. Tying the IRS2003 inputs together and driving them with a single PWM signal should provide similar functionality to the IRS2004 single input device, per the hyperlinked datasheets.

The discrete inputs on the IRS2003 gives you the flexibility to manually adjust the deadtimes higher than what's provided by the IC itself, and give you complete phase control over the outputs.