Doing the math-
Toroids Chart - http://toroids.info/FT50-75.php
Active wire loop 1.5M dia.
EFHW 80-10M -one to try. Half-wave, loading coil near feed end. http://vk3il.net/projects-antenna/multiband-end-fed-80-10m-antenna/
"The inductor was wound on a 22mm PVC former (a piece of 20mm pipe) with 17 turns of the antenna wire located 2m from the feedpoint. The coil was held in place by drilling two holes in the former about 30mm apart and passing the antenna wire through them from the inside. The whole coil was then covered in heatshrink tubing to hold the turns in place. The final coil measured 4.45uH.
The wire was cut to 40m length and then trimmed when set up as an inverted V to minimise the SWR at 7.090 MHz (you could of course optimise for any preferred frequency). In my case, it ended up at 39.21m, but this will vary depending on the specifics of the setup etc."
Toroid Core Calculator - On-line handy dandy calc the value of those unknown cores. http://coil32.net/online-calculators/determine-toroid-core-permeability.html