I just checked the code of pax logging, it doesn't export the org.slf4j.impl package in the pax-logging-api as pax-logging is not want to expose the implementation of the other logging system. To achieve this pax-logging did some customization on the impl class to let is leverage the pax-logging-services which is based on log4j.
So I doubt you can use slf4j-ext.jar out of box in servicemix even you deploy it as an OSGi bundle.
If you still want to implement this kind of feature, you may need to buy some commercial support or do it yourself.
This turned out to be an issue of versions. I was using the latest versions of slf4j-ext.jar, and trying to deploy it, but the FUSE components were searching for a specific version.
Once I deployed the right version, everything came together.
I checked the code of the Profile.class. It doesn't have any dependency of org.slf4j.impl.*. But I don't know if your slf4j-ext.jar needs to import the package of org.slf4j.impl ?