This is a great thread. I know it can feel awkward sending an offer at such a low price, which is why I try to ask the listing agent if there's any flexibility on the price before moving forward. What really pisses them off is when you send a contract with no context or conversation beforehand with a super low price (relative to listing price). They have to open the email, then take the trouble to open a PDF and scroll to the purchase price section only to find a super low number. It's so much work (sarcasm).
So, my thoughts on this for you moving forward, shoot the listing agent an email just saying: "Hi, I saw your property on XYZ street and I'm interested in sending you an offer on it. Does your seller have any flexibility on the price? I see it's been sitting for at least three weeks now and it looks like it needs some work, which is fine with me. I'd be paying cash or using hard money. If you're interested, you can represent me to get the buy-side commission." Keep it short and sweet. See how they respond, and then respond back with a super low price range to anchor them. Then if they won't represent you, you can use your agent to send the offer if they think that's a good idea. The sad reality is that you'll only get a low offer past a listing agent if they take it seriously, which they will once you massage them and get their guard down. I know it's not as efficient as blast emailing (a story for another time), but it's a little more personal and effective. Go lock up some deals! Good luck!