There are a ton of balanced tuner designs on PA0FRI's site.. good for wire loop antennas and balanced dipoles and similar.
See what your "electrically rotateable" wire antenna options are.
Also, keep in mind my lack of real world, practical experience.
Get as many others advice as possible.
Especially remember simple is often the best.
As I said, a balanced antenna (or balanced mag loop, the simplest uses a double ganged variable capacitor to tune the loop with the center /body part grounded, and a shielded and/or balanced pickup loop) is said by many to offer big noise advantages. I only have experience with a not well balanced mag loop and my occasional (arguably lame) attempts to make a balanced antenna by using two wires in my back yard.. trees being used were/are not well placed for this..
Still both were quieter than my long wire, even with its unun (which reduces noise quite substantially).
Some lengths of wire (search term "end fed antenna") tune up easily on all bands because the length of wire and feed line are optimal for this. Sometimes the wire ends up being a manageable match on all ham bands using a 9:1 unun, so much that you don't need a counterpoise or can get by with a very basic one.
With some lengths of wire and coax feed. A lot has been written about this and its worth reading.
With the right length wire, a 9:1 unun and feed, you may find that your antenna "just works" with little fuss and only the rigs' own antenna tuner or a very basic tuner..
Zap.. problem solved with very little effort..
Misc links- hope some are helpful!:
http://www.nonstopsystems.com/radio/frank_radio_antenna_magloop.htm (This is a huge article about mag loops - unique for its definitive list of loop coupling methods, especially)
http://www.66pacific.com/calculators/small_tx_loop_calc.aspxAlso:
https://m0ukd.com/static/homebrew/magnetic_loop/rjeloop1.exe and
https://m0ukd.com/static/homebrew/magnetic_loop/rjeloop2.exehttp://www.aa5tb.com/loop.htmlhttp://www.pa0fri.com/ (lots of antenna tuner info including "s-match" balanced tuner
This is kind of interesting.. very large loops designed for very low resistance..
https://web.archive.org/web/20170108145422/http://www.g4hjw.metahusky.net:80/magloops.htmThere is also a long essay about "The Underestimated Magnetic Loop Antenna" by VK5KLT out there.. Google should find it.
Also, I have a PDF "Chapter 10: Large Loop Antennas" - about wire loops (and their HF characteristics) that appears to be from a book on ham antennas.. Maybe Google can find it.
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End-fed/off center fed/Windom
http://m0ukd.com/homebrew/antennas/homemade-carolina-windom-antenna/http://m0ukd.com/homebrew/baluns-and-ununs/end-fed-half-wave-antenna-tuned-coupler/