You should be able to do constructor injection, something like

public FullSearchIndexJob(IServiceProvider serviceProvider, LocalizationService localizationService, IndexBuilder indexBuilder)
{

Quan, I'm not following. How does your example relate to Mathias solution?

By parameters I suppose you meant settings. You can add an Options object which can be set via appsettings.json as a constructor dependency to your scheduled job. 

In this case I'd have created a new block type with relevant settings and assign it to a content reference on start page. The job can easily locate the block and use the settings there. It is not as convenient as the plugin you shared but would do the job.