I really don't think you're going to do better than $38/month with DirecTV. It's been years since I've had them, but I was always able to negotiate further discounts whenever a promotion ran out - they would always discount deeply to avoid losing a customer. If that's still the case, that's your best bet.
We haven't used Sling in a while because it was far and away the worst streaming TV option - loads of buffering and disconnects. Hulu TV is ok, Playstation Vue is great, Youtube TV is quite good. All of those options are more than what you're paying for DirecTV, though. From what I recall, each streaming service had its own agreements with local channels, and I think PSVue was the only one we could get that had them all (and it was of course the most expensive). And also, a quick Google search tells me streaming services can range from 1 - 3 GB per hour of HD TV, so unless you are planning to stream in SD only, you'll eat through that 100 GB pretty fast.
I think your best bet is sticking with DirecTV and negotiating the best discount you can get by threatening to cancel so you don't risk racking up tons of overage charges if your DH really has the TV on all the time. If you do decide to switch to a streaming service, at least get an antenna. Antennas are a whole 'nother rabbit hole when it comes to cutting your TV service, and given you're out in the country you're probably gonna need a big antenna, but there are options. Check out
TV Fool. It lets you put in your address and tells you exactly what kind of antenna you will need for the channels you want. You'll probably need a pretty high-powered antenna you can put in a high place, maybe in the attic or bonus points if you can mount it to your roof. You may or may not also need a signal amplifier - this takes some trial and error.
Oh yeah, this is taking me back. Good luck if you decide to go the streaming route! I can help if you have questions, I got way into this stuff. We are lucky right now because FiOS is included in our rent at our current apartment, but if/when we move the FiOS is getting dumped and we're going back to streaming/antenna.