If the 3D is working, crosstalk will be only in one eye (or at least much more obvious in one eye). Essentially, you should be able to change your viewing angle and distance to find a sweet spot. As you do this, the screen will flash and the image should flash and the images swap places in parallax, as your brain is figuring out what’s going on. The lines you should see flashing vertically as you do this are the parallax barriers. If your new screen doesn’t have these, it can’t display 3D images.
I think N3DS has technology to change alignment by tracking your head? If so, it shouldn’t be an alignment issue. Though you can experiment by rotating the 3DS slightly clockwise and anti-clockwise to check that it doesn’t make it better or worse.
Assuming you’ve messed around with the calibration, or if the 3D isn’t working at all, it might just be a bad or 3rd party screen, a 2D screen, or even something as simple as replacing or freeing up the ribbon cable.
There are also 2 types of screen in 3DS’ and I’m not sure how to tell which is which. There’s a small chance that you might be more susceptible to crosstalk on one over the other.
Hope you work it out! I get 3DS anxiety every time I turn mine on. Parts are getting scarcer and there’s currently no 3rd party alternative, unlike every other handheld.