how to use log4j-to-jul with log4j-web

Hi All:

I have a web application that uses log4j (v2.20) which runs inside 
Tomcat 9.x on Java 8.

Currently, the WEB-INF/log4j2.xml configuration file in the application 
sends its output to a rolling file appender targeting a separate file on 
the file system, but what I'd like to do is make all log4j output go to 
the regular per-application log under ${catalina_base}/logs which is 
managed by the stock Tomcat JULI implementation.

We now have the log4j-to-jul module which can adapt log4j 2 output back 
to java.util.logging.
Similar to my understanding of the purpose for log4j-to-slf4j, it seems 
that log4j-to-jul is meant to be used as an implementation by itself for 
log4j-api and without log4j-core.

The application currently uses log4j-web to get the all the essential 
setup for initializing log4j 2 under an application container. The 
log4j-web library appears to have a hard dependency on log4j-core.

After adding log4j-to-jul to the application classpath, I can see that 
it is recognized:
> Multiple logging implementations found:
> Factory: org.apache.logging.log4j.core.impl.Log4jContextFactory, 
> Weighting: 10
> Factory: org.apache.logging.log4j.tojul.JULLoggerContextFactory, 
> Weighting: 20

But then the following error is reported:
> ERROR StatusLogger LogManager returned an instance of 
> org.apache.logging.log4j.tojul.JULLoggerContextFactory which does not 
> implement org.apache.logging.log4j.core.impl.Log4jContextFactory. 
> Unable to initialize Log4j.

In org.apache.logging.core.config.Configurator, line 47 there is a 
conditional that checks the return type of the logging implementation 
is-a Log4jContextFactory. The problem is then that 
JULLoggerContextFactory implements only LoggerContextFactory.

I'd like to keep my tomcat container as stock as possible. Particularly, 
continuing to use the built-in JULI per-application logging and *not* 
switching the entire container to use log4j as its logging implementation.

Can anyone suggest how I can use log4j-to-jul successfully for my use case?

Thanks,
Jason