I usually strong name my assemblies because I don't want to discover it later on that my assemblies needs a strong name, just in case the assembly is being used in some other way than I originally intended.
I've also had some problems relating to events in Sharepoint where reflection is used to execute functions based on class and assembly info (probably stored in database), so if you add a strong name later on then you have to update the places where the old event was used (e.g. on lists), otherwise your functions won't get hit. On the other hand if you have a strong name then this is easy bu using web.config assembly redirect
I like your idea though of having the assembly in bin, that way you can use CAS which provides more control for administrators.
To resolve this problem then you could start out by adding the strong name and deploying the asembly to the GAC, then add your .webpart (or .dwp) to the web part gallery. If that works you can try moving the assembly to the bin folder and then remove the strong name.
You might consider deploying the webpart in a feature and add the code neccessary to add the .webpart file to the gallery on the fly so you dont have to worry about the file, this can be accomplished by using code using a feature receiver
using (SPWeb web = site.OpenWeb())
{
web.AllowUnsafeUpdates = true;
site.AllowUnsafeUpdates = true;
SPList list = web.Lists["Web Part Gallery"];
SPFolder root = list.RootFolder;
SPFile spFile = root.Files.Add("ContentEditor.dwp", s);
spFile.Update();
}
or by using caml xml
<?xml version="1.0" encoding="utf-8"?>
<Feature Id="8425EAF8-6GBE-4698-83C7-831CA8614D6D"
Title="WebPart"
Description="Some description"
ImageUrl="GenericFeature.gif"
Scope="Site"
xmlns="http://schemas.microsoft.com/sharepoint/">
<ElementManifests>
<ElementManifest Location="elements.xml" />
</ElementManifests>
</Feature>
<?xml version="1.0" encoding="utf-8"?>
<Elements xmlns="http://schemas.microsoft.com/sharepoint/">
<Module
Name="WebPart"
List="113"
Url="_catalogs/wp"
RootWebOnly="TRUE">
<File Url="WebPart.dwp" Type="GhostableInLibrary" />
</Module>
</Elements>