I gather I can build a loop of wire that resonates at 60KHz, put it in
my attic, and it will reradiate the signal. Does that sound right?
Won't it have to be big - the wavelength at 60KHz is 5000 meters!

It will create a resonant field and concentrate the 60KHz energy in your
house.

You can use a multi-turn loop. Square, 4-turns, maybe 2M per side and an
AM tuning capacitor.
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Just a construction hint. For a neat multi-turn rx loop you could consider
ribbon cable as used in computing gear .
Some time ago ,at a fleamarket I bought a roll of 100 ft (30.5 metres) of 15
leads wide ribbon cable.

Example : To make a 4 turns loop as above you would need 2*4 equals 8 metres
of 8 lead ribbon cable using end of lead 1 and 8 as ends of the loop , join
ends of lead 2 and 3 , 4 and 5 , 6 and 7.
Although the ribbon leads multi-strand overall diameter is only 0.2 - 0.3 mm
,it should be OK for rx purposes.

Frank GM0CSZ / KN6WH