This is right. I'd even cut out "I will be brief".
If you've already reached the person, the e-mail below is more of your flavor.
If I sound like a dick, it's only because I want to be as direct as possible:
Nobody cares about what you want, your business, or your promo. Write all of your cold e-mails understanding this. You want to introduce value, not a service. Imagine the person you're writing to just deleted 12 spam e-mails from Chick-Fil-A and Wrangler Jeans from their inbox. What separates you from the rest of the shit that they (and I) get on a daily basis is that your e-mail is digestible and enticing. You also don't want to sound like a robot.
Think of fine dining - you get less food for more money, but the damn thing is cooked to perfection and looks it's a piece of work you need to hang on the wall. Your e-mail has to be that dish.
Don't thank people for taking their time to read your e-mail, and don't "hope for" working together. Earn their business and have them earn your service.
The biggest problem overall is that the e-mail looks like an e-mail or essay - not a conversation. You want them to feel like they're talking to someone else on the other side of their screen.
Lastly - and I feel like I'm jumping on the pile here - don't attach something they don't ask for. You're asking them to help you make money without talking to someone on the phone? That's a dream.
Subject: ATTN: ____ , for cleaning the "name of building".
Other buildings in your area keep using our cleaning services because of our customer service and guarantees. Our employees are rewarded based on reviews, which ensures that our partners and our employees stay happy. Check out ________ if you'd like to see reviews.
We like to brag that we get the job right the first time, but if you're dissatisfied with any of our jobs, call us the next day and we'll send someone over to make sure you're taken care of.
If you're free _____ morning around ____AM, I can give you a ring to learn more about some challenges and expectations you have with keeping your business clean. Is this fine, or would a better time work for you?
[Name of company]