I've found a very fast way to earn crowns. This does involve grinding but what other get quick scheme doesn't? Anyways what you do is you run the first floor of Snarbolax on elite. This earns 800-900 CR per run and also yields 2-3 Monster bones which puts your net earnings at about 1000 CR per run. I have a Final Flourish and running the first floor killing all the monsters only takes me about 4 or 5 minutes. So in 4 minutes I've made 1000 CR. Run this for 20 minutes and you've made 5000 CR.
Anyone have any faster ways?
Your optimal farming strategy depends on your playing level. Your post is valuable because it applies to near-beginners.
An expert party can run Firestorm Citadel in 30 minutes or less. If they kill everything then they earn about 9,451 + 300 + 3,000 = 12,751 crowns. If they skip some monsters then they probably still earn over 10,000 crowns. So that beats your 5,000 crowns per 20 minutes.
Operation Crimson Hammer has a similar overall payout if you have extra 5-star orbs and you vendor Perfect Mask of Seerus. I don't know how quickly players can run that mission. One old post claims similar times for OCH and FSC.
(And while your calculation seems to include the value of materials found, these calculations don't. So their actual profitability may be higher.)
You might do a Google search for "earn crowns site:forums.spiralknights.com" (without the quotation marks), and then focus on threads that take time into account. (A lot of advice that you'll find, such as my FAQ on earning crowns, doesn't take time into account.)