Agree with your model over a 2 year period but it doesn't work for 5 years straight of high harvest.
If you killed 180,000 plus out of 500,000 year one you could, based upon recruitment do it a second year with an even lower starting population but you could not sustain the same 180,000+ for the subsequent years of 3-5 because the starting population would continue to diminish. We in fact actually reversed your model
and increased the harvest substantially years 3-5.
Our increased harvest trend started in 2006 and continued though 2010. Do you really think that each years previous harvest starting in 2006 reduced the population to where there were fewer than 500,000 deer starting 2009 when we had the highest harvest ever at 261,000 and then were able to follow that with 239,000 in 2010?
2004- 216,000
2005 - 209,000
2006 - 237,000
2007 - 232,000
2008 - 252,000
2009 - 261,000
2010 - 239,000
If the starting population was way north of million deer in 2006 your explanation would fit well with the historical data.
Or the deer recruitment was higher in previous years than it is today.
I think we will just end up agreeing to disagree on this.