I don't know what new things are available now that might do this. The best thing you can do if you want a unique drum sound is to record your own samples. There also are (or used to be) a lot of free or cheap sample packs from acoustic kits.
I feel the same way as you about overused modern drum samples; I still use an old copy of Fruity Loops from over 20 years ago because it lets me drop in my own stereo samples and build a "kit" from my own hits instead of being stuck with some new school sample library. Maybe you can do the same thing with a newer and more convenient piece of software. I know that some modern programs go really deep as far as virtual mic placement and stuff, you could probably mimic almost any sound if you put the time in. I really hate the actual process of programming hit by hit on FL, it's tedious and extremely slow. But, here's how I approach it.
The first key to a more realistic sound is to have a lot of different hits on each drum and cymbal, some at different levels of intensity, but also with several hits at around the same intensity so you're not stuck with exactly the same sound for each hit during a given beat. The more the better, although again, the more samples you have, the more tedious the process gets. For example, I've got 12 different snare hits in the FL "kit" I'm using now. Samples 1 - 5 are hard hits that I can use as single hits during any given beat, and then they get progressively softer, with 6 - 9 being less aggressive hits that I can use in a snare roll, fill, or single hit in a softer part, and 10 - 12 being even lighter. The only time I'll use the same hit a few times in a row is for blasts, on one of the softer samples. This kind of variation is really important in the cymbals - you want a few different aggressive hits and then a few that you can use in sequence to mimic "cymbal bashing" without repeating the same sample every time, or even every other time. I have something like 15 different ride hits, for instance, on different parts of the cymbal and so forth. Also give yourself a few different cymbal chokes and hi-hat drops that you might use very sparingly. The more variety the better. If you're in a pinch for variety, you can duplicate a hit and pitch shift it very slightly up or down so it doesn't have exactly the same resonance.
The second key is to export your finished drum tracks as audio and mix them like you would the tracks from an acoustic kit. When I'm doing a final mix, I'll have separate tracks for kick, snare, cymbals, toms, ride, and hats, going to a group buss where I can add overall effects like reverb, compression, distortion, etc. For a lo fi sound you'd probably want to roll off the high end a bit and play around with tape emulation and room reverb. You can also record the finished drum tracks with a microphone in the room and blend that sound back in. There's really a lot you can do to distress the sound. They'll always sound a little stiff but it's better than not having drums on your song.
This isn't a lo-fi recording but it's the most recent finished thing I did with programmed drums, as an example of what I'm talking about. Listening back, there's some stuff I would do differently, but I'm pretty happy with how it turned out.