You should strive better to get comps. At least you acknowledge you've tried. But you've got to get a handle on the value.
Next: Don't worry about being "insulting." I hate that term. Hate it with a passion. Don't worry. You make an offer. Let the owner decide whether it's insulting. I've seen some sellers consider an offer of just a dollar below list consider the offer insulting. I've seen other sellers welcome an offer 20% below the listing price. Unless you're a mind reader, you won't know what the owner might or might not consider insulting. Besides: What's the worst that can happen? Is the owner going to challenge you to a duel at high noon? No? The worst that will happen is the owner says "no." The next worst is he says "yes." (That's bad, because it means you offered too much.) The best is that he counters.
Which gets to a "lowball" offer. That, too, is in the eyes of the seller. All you should be concerned about is a number that works for you. By the way, an offer of 7% below list when a house has been on the market for 5.5 months isn't a lowball. Without knowing any further details, that likely would be offering too much.
One problem you may be facing, though, is that the owner (if it's not a short sale or foreclosure) can't go any lower. There probably isn't much equity in a home that was purchased in 2005 or later. So, let's say someone paid $300,000 in 2005. Back then, you could get 100% financing, so they might owe $300,000. Even with 20% down, they'd owe $240,000. Today, that property could well be worth about $250,000. Maybe less. So they put it on the market at $275,000. They get no offers. But (depending on how much they put down) they're either breaking even at $275,000 or losing money. And we know it's worth nowhere near $275,000, so they get no offers.
A Realtor can look into the situation, give you some additional information, and suggest some strategies.
Hope that helps.