I worked it out, and here are the details:
First, there's no way to specify file includes or excludes if you use the built-in assembly descriptor jar-with-dependencies.
The assembly plug-in documentation gives the sample jar-with-dependencies descriptor here.
I copied and pasted that descriptor to a file in my project directory called exec-jar.xml. Then in the pom, I changed the assembly plug-in to reference that descriptor. Here's the excerpt:
<build>
<plugins>
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-assembly-plugin</artifactId>
<version>2.2-beta-3</version>
<configuration>
<descriptors>
<descriptor>exec-jar.xml</descriptor>
</descriptors>
<archive>
<manifest>
<mainClass>com.package.MyMainClass</mainClass>
</manifest>
</archive>
</configuration>
<executions>
<execution>
<id>make-assembly</id>
<phase>package</phase>
<goals>
<goal>single</goal>
</goals>
</execution>
</executions>
</plugin>
</plugins>
</build>
That bit of descriptor binds the assembly to the package phase of the life-cycle, and references the exec-jar.xml descriptor. Doing that package confirmed that the jar was built just as it was with the predefined descriptor.
So then it becomes a matter of modifying exec-jar.xml to exclude the CXF files that conflict with the Spring files. Here is my assembly descriptor that accomplished that:
<assembly>
<id>jar-with-dependencies</id>
<formats>
<format>jar</format>
</formats>
<includeBaseDirectory>false</includeBaseDirectory>
<dependencySets>
<dependencySet>
<unpack>true</unpack>
<unpackOptions>
<excludes>
<exclude>cxf*/META-INF/spring.handlers</exclude>
<exclude>cxf*/META-INF/spring.schemas</exclude>
</excludes>
</unpackOptions>
<scope>runtime</scope>
</dependencySet>
</dependencySets>
<fileSets>
<fileSet>
<directory>${project.build.outputDirectory}</directory>
</fileSet>
</fileSets>
</assembly>
Now here's the rub. If you do this with the currently released assembly plug-in, version 2.1, it will fail on the tag as "unexpected." The tag is supported in unreleased version 2.2 of the plug-in. Note in my pom file excerpt above, I specify maven-assembly-plugin version 2.2-beta-3 which was the latest at the time of writing.
This successfully built an executable jar, and Spring had all of the handlers and schemas it needed to initialize my app.