Welcome to the forum, and I’m sorry to hear about the loss of your Edwin. If you want you can always post a picture here to have a little memorial. I’m sorry that I can’t give you advice re: E. Cuniculi, but there are several people here who sadly have had experiences with the disease.
Just wanted to say welcome and applaud you for being such an awesome pet owner! We get a too many people here who fail to do their research properly before they get rabbits. It’s always really refreshing to see someone who respects rabbits so much ^_^

Bombur was just diagnosed with EC, and our vet told us that Asriel could get it through Bombur’s urine. She also said that a lot of bunnies are born with it, but are asymptomatic and never show symptoms.

My back was acting up so I decided to make myself useful researching your question while laying in bed
Your search results will be better if you include the word “spores”, because that’s the form the parasites take to survive outside their host. This is what I found:

http://www.dierenkliniekwilhelminapark.nl/dierinfo/konijn/cuniculi.html
This resource says:

“De sporen kunnen 2 weken overleven bij kamer temperatuur en zelfs weken tot maanden bij een vochtige en warmere omgeving. Mocht uw konijn komen te overlijden maak dan het hok goed schoon en ontsmet het. Om besmetting naar ander konijnen te beschermen kun je het hok schoon gaan maken om de sporen te doden met 0,1% bleek of met 70 % Ethanol.”

Translated:
“The spores can survive at room temperature for up to two weeks and even longer in hot and humid conditions. Should your rabbit pass away clean out the hutch thoroughly and disinfect it. To prevent reinfection of another rabbit you can clean the hutch with a bleach solution or a 70% alcohol (ethanol) solution.”

https://www.ncbi.nlm.nih.gov/m/pubmed/16368193/
This article mentions how long you should apply the cleaning solution to the spores to make sure they are destroyed.

https://www.wormsandgermsblog.com/2010/04/articles/animals/other-animals/eliminating-e-cuniculi-in-the-household/
Here’s another website which talks about removing the spores from household items.

Sorry to hear about Asriel and Bombur, I hope they’ll be healthy and safe again soon!

There is also evidence that EC spores can survive being frozen outside, so they are capable to lasting many months. I think it all depends on the environment and if conditions are ideal for survival. Two weeks might be accurate under certain conditions, but not all. That being said, most rabbits are exposed to EC at some point in their lives. The vast majority never exhibit any kind of symptoms. Who is to say your would-be new bunny hasn’t already been exposed? If that is the case, then it won’t matter if spores are present or not. So I wouldn’t worry too much about it. No need to stress yourself needlessly. Of course, it certainly doesn’t hurt to thoroughly clean everything before bringing the new bunny home either.

You’re welcome!
Some tips from a chemical engineer here: when you clean the hutch, do so while ventilating the house. For proper disinfection you’ll be using large amounts of strong cleaning agents which are irritating to skin, eyes and lungs. Use personal protection like gloves, don’t smoke and wear old clothes. If you have (safety) glasses around, use them. Be careful with concentrated bleach because it will ruin fabrics, and under no circumstance mix it with anything else than water, this can create toxic gasses. Ethanol is highly flammable and will evaporate, if you use a lot of it in one room it’s a fire risk. Keep all ignition sources away, don’t smoke and ventilate the room well.