Many modern HF rigs can be modified to transmit throughout the HF spectrum, often by a simple adjustment. It is doubtful whether any of them will do `general coverage transmit' to the same lower frequency limit as the general coverage reception capability.
Having a few idle moments, I just made a quick check:- CW, 10 dB S/N -81 dBm [400 Hz filter installed] FM, 12 dB SINAD -72 dBm AM, 10 dB S/N -61 dBm Unsurprisingly, the preamp makes ZERO difference. The test equipment I used is an IFR 1200S, which although calibrated, may or may not produce valid results at LF :-)
Simon Lewis (GM4PLM) says the IC706 covers this band too.
The TS450S (and presumably the TS690S) covers down to 30 kHz on receive. Richard Lamont (G4DYA) (yup, it's me) did a quick and dirty measurement of the receiver sensitity, and got a figure of -115 dBm for a 10 dB S/N (SSB) at 73 kHz. I didn't try CW as I didn't have enough attenuators!
One person who has taken me up on this offer is John Hey (G3TDZ). He sent me some notes and drawings on an experimental transceiver.