I've played around extensively in the past using small air loops and ferrite bar loops to DF at HF. Both will work very well at these freqs with a couple caveats. You will get the best results if the loop is outdoors; there's seems to be too much obfuscation of the null bearing when the loop in inside, possibly from re-radiation from metallic house structures and wiring. If you are using an air loop, it is best that it has a balanced architecture with a balanced amp to get the deepest nulls.
The ferrite bar is the easiest way to go for a quick hack. Throw 30 to 50 turns on it, find a variable cap that resonates it at the freq of interest. Throw a second winding on the bar which has maybe 5 - 10 turns, and connect this to your receiver. It's cheap and quick, and you can always optimize the turns in each coil by testing it against top-end MW stations.
I don't see sig strength as being an issue; you're going to hear it or not. As I understand it, these beacons are pretty intermittent in nature. It's probably going to take some patience to find the null.
If you're really serious about DF'ing these freqs, the amplified air loop is the way to go. It will give generally reliable results up to around 2.5 MHz. In fact, the only time I logged the Falkland Islands (2380kHz) was with a small air loop. I had a rotor on it at the time. I only got about twenty seconds of audio, but I was able to DF it to within about ten degrees. They QSL'd it! Not a brag; I just got damn lucky that night. Rather, I think this is indicative of the enormous potential of small loops.
There are quite a few published articles about amplified air loops around. Might I suggest looking at some of the impressive work that Mark Connelly has out there. Most of it is geared towards MW, but should be easily modified to work just above the MW band.
Have fun!
BTW, what are the typical signal strengths you're seeing with your current antennas?
