Since I live here, I have never looked too deeply into the specifics of Iowa's non-resident license application. I know it is an expensive and time consuming process. Enough so, that it has kept my out of state relatives and friends from hitting me up for a hunt. I think you will need to be patient.
Secondly, please remember that individual results may vary. Most of those "Iowa giants" are on well managed private lands. Do not invest the time and money if your happiness is dependent on killing a B&C. The TV hype and the reality of hunting public lands or small private parcels in Iowa and two different things.
All that being said, if you want to come see some beautiful Midwestern scenery and have a chance a decent deer, it can be well worth the effort. I live in South Central Iowa and Steven's Forest is the largest public hunting in the area. There are a number of units spread over 2-3 counties. As long as you do not mind modest lodging, there are plenty of small town motels to choose from. Bow hunting, particularly during the week should offer you a fairly private hunt. Does should be plentiful and targeting a 2.5-3.5 year old buck between 110-130" would be a realistic goal. Of course B&C bucks are not out of the question, but they are far from common.
Hope that helps.