I know you said you aren't going to be wholesaling the property, however, you're going about this like a wholesale deal. So a couple things.
1. When someone says they want to "close fast" or "sell now". That means absoutely NOTHING. Because every single seller wants to sell as soon as possible. No seller lists their property and wants it to sit on the market for 4 months. They are selling because they literally want to sell and they want it to sell as soon as possibe. So don't get to caught up when someone says they want to sell now, because that is every single seller in the market.
2. If the seller has a contract with the realtor to list the property then you CAN NOT negotiate with the seller directly. From what said it sounds like, this realtor is not a dual agent. He/she is only representing the seller I assume? That being said the lower the offer you make the less the agents commission will be. Your only option to avoid the realtor fees would be to wait until the property becomes an expired listing (if it doesn't sell) and then you are free to talk with the seller directly.
3. Is your offer out the ball park? I don't think so, but it doesn't matter what I think. What matters is whether the seller accepts or not. Make the offer, worst case it's declined. No big deal.
4. I am very confused with your numbers that you say are "saving" the seller money. A seller who lists a property with a realtor isn't that pressed for time on selling the property, so trying to get a price discount by claiming to be saving them time probably will not work. Also, you said the property is being rented on a month by month basis so at this time there is no rental loss.
At the end of the day just make the offer that works for you. There is no harm in doing that. I don't know why a realtor called you when the property isn't listed on the MLS. I'd figure out if there is a realtor in the negotiation or not.
Hope this helps
Brandon