Partial Binding, wrong .dll, mismatched x64/x86

When I publish my .NET web application to its deployment folder, it publishes a required .dll fine. However, this .dll file requires 2 other .dll files. These other two are older versions and cause an error. If I copy and paste the new versions of the .dll files to the /bin folder at the deployment location, everything works fine.

I figured the new versions fix some sort of x86/x64 compatibility issue because I get problems similar to this SO question when I use the old versions. I also get this warning about partial binding:

=== Pre-bind state information ===
LOG: DisplayName = myDll
 (Partial)
WRN: Partial binding information was supplied for an assembly:
WRN: Assembly Name: myDll | Domain ID: 2
WRN: A partial bind occurs when only part of the assembly display name is provided.
WRN: This might result in the binder loading an incorrect assembly.
WRN: It is recommended to provide a fully specified textual identity for the assembly,
WRN: that consists of the simple name, version, culture, and public key token.
WRN: See whitepaper http://go.microsoft.com/fwlink/?LinkId=109270 for more information and common solutions to this issue.
LOG: Appbase = myDeploymentLocation
LOG: Initial PrivatePath = myDeploymentLocation\bin
Calling assembly : (Unknown).
===
LOG: This bind starts in default load context.
LOG: Using application configuration file: myDeploymentLocation\myApp\web.config
LOG: Using host configuration file: C:\Windows\Microsoft.NET\Framework64\v4.0.30319\aspnet.config
LOG: Using machine configuration file from C:\Windows\Microsoft.NET\Framework64\v4.0.30319\config\machine.config.
LOG: Policy not being applied to reference at this time (private, custom, partial, or location-based assembly bind).
LOG: Attempting download of new URL file:///C:/Windows/Microsoft.NET/Framework64/v4.0.30319/Temporary ASP.NET Files/myApp/e2de69d0/f42308b3/myDll.DLL.
LOG: Attempting download of new URL file:///C:/Windows/Microsoft.NET/Framework64/v4.0.30319/Temporary ASP.NET Files/myApp/e2de69d0/f42308b3/myDll/myDll.DLL.
LOG: Attempting download of new URL publishLocation/myApp/bin/myDll.DLL.
ERR: Failed to complete setup of assembly (hr = 0x8007000b). Probing terminated.

I tried manually referencing the new versions of the dependent dlls, rebuilding the parent dll, cleaning solutions, restarting VS, looking in GAC for the files (but not finding any of them).

What did I miss? Or as a workaround, is there a way to make is the .dlls be overridden with the newer version at the end of the publish?