Issues occurring when transitioning code updates into a load-balancer situation

I'm a seasoned ASP.NET developer (15+ years) and Episerver is new to me as of just about two months ago.  I did the week-long developer training and then was asked to extend an existing page's class with a new property.  This easy code change got a "pass" from our internal QA staff, but QA doesn't test in a load-balanced environment.

Our setup has two web servers intended for public use, and a "content" server intended for internal use.  The major difference in configuration is that the public pair doesn't allow CMS logins.  So, upon deployment, the code got pushed to the content server and one of the public servers.  Obviously, all three point to the same database.  Upon trying to edit the new property on the content server, we saw an error message when trying to save the page, basically saying that the property didn't exist.  This wasn't a show-stopper, and about a week later the message disappeared after the second public server was updated with the same code.

I'm suspecting that the differing codebases caused this issue, with two servers trying to make the property available in the database, and the other server potentially trying to remove it.  Is anyone familiar enough with this to lend some advice?

Thanks in advance!