It's not true that the OE headlights are inadequate.
I'm going to strongly object to that statement. Quite frankly, I find the headlamps on my daughter's CR-V to be a throwback to the 'dark ages'. The root cause of the problem is the combo H4/9003 bulb. The low beams are OK. The pattern and cutoff of the reflector assembly is typical of this older design. Incandescent bulbs in projector housings are typically better, but I can live with these. Slightly better bulbs help. But they don't help for long due to tungsten darkening. I'm now in the mode of replacing her bulbs every 18 months or so.
The high beams, unfortunately, are pretty poor. And the use of the high beam filament as a DRL degrades the entire system by depositing tungsten on the inside of the envelop. Take out your bulbs and observe the black film that's stealing your light as they age. I'll post pictures of the ones I took out last year if you aren't convinced.
Most modern cars prior to the introduction of LED lighting use the "4 lamp system". Dedicated low beams and high beams. When you turn on the high beams, you also retain the wide/low spread of the low beam bulbs. They illuminate the mid-distance range, and are particularly useful for driving in dark hilly areas when cresting a hill. When the high beam distance pattern 'lifts' off the road, the low beam pattern fill in. On the 2012-2014 CR-V you are left with a huge dark region until the nose of the car points back down again. That's unacceptable in heavily populated deer areas.
We had similar H4 dual filaments on our old Odyssey, but the problem was easily solved with a minor wiring modification. Those housings were larger and able to handle the heat. I've been advised that the smaller housings of the CR-V cannot.
In the 2015 facelift, Honda addressed this shortcoming, and went to a 4 bulb system. Drive the two back to back, and the difference in illumination is striking!
So, what to do about it....
1) JDM or EDM enclosures are NOT the answer, as the beam patterns are too different from FMVSS/DOT. Illegal and potentially dangerous.
2) I hate rebased HID conversion kits. Glare city, especially in reflector housings. The 'filament' (gas discharge) is in the wrong spot. LED bulbs are generally no better, as no two makers align the LEDs the same, or correctly.
3) An entire Projector transplant could be done. Again, it likely won't provide separation of high and low patterns.
4) There are aftermarket headlamps available (Anzo and others) that pack two projectors into the space on each side. No data on quality or pattern integrity available.
5) I did look at if it's possible to swap in the grill & lights from a 2016 into a 2013. Maybe.... and a lot of cash outlay to try it. The fit looks OK, but without a full set of mechanical drawings, it's a gamble. I occasionally look for a junk yard find, and maybe over time I'll 'collect' all the parts required to try it.
Or... I'll just dump the car and move on....