The issue you will face is that, with the itinerary you've presented, your visa application will be refused. Under the Schengen rules, you must apply to the embassy of the country which is the main destination for your trip. In this case, it's unambiguously Germany. The Schengen rules were formulated to prevent 'visa shopping'. That is, applying to the state who you think will look most favorably on your application.
What's to stop you presenting an itinerary for a month long stay in Iceland, and then deviating from this itinerary to spend most of your time in Germany? Theoretically, not much. But you will be questioned at the border when you enter Iceland. If you are found out, you will be sent back where you came from. And getting further Schengen visas will be extremely difficult.
What can you do instead? If you really don't want to apply to the German embassy, perhaps think of genuinely changing your itinerary so that you are able to apply to a different state. Also bear in mind that a month stay is quite long for a holiday. A shorter itinerary may be less likely to face problems. Once you have established a record of complying with your visa conditions, longer stays may be more likely to be granted.