Basically our application is using a custom JavaFX skin. The solution was to add this as a control in:
"C:\Program Files (x86)\SmartBear\TestComplete 12\Bin\Extensions\ThirdParty\com.smartbear.testcomplete.thirdpartycontrols.javafxcontrolssupport.xml"
Because of this, we can't store this configuration at the project level like most things, so that means updating all of our VMs that run tests. This also will require intervention with any updates to Test Complete or Test Execute.
Having this be configurable at the project level would be a huge benefit.