https://qsl.net/xe1cdx/Hamdocs/10/10 mts Loop.pdf
Increase these lengths by about 4% should make this fall in for SSB on 27.400
About 2db gain over a dipole and a
slightly more gain than a standard single square loop (1.7dB over dipole) but lets not get picky
Shrinking the loop to 3 x 4 ft is over 60% below resonate 50 Ohm length...
No simple Balun, I would think will bring that small of length into Transmit range.
Going to need a lot of capacitance to bring that into where it will load I would think.
Adding a Air-Variable cap
may bring it into play(much like tuning a Mag-Loop antenna) but the spacing on the plates of the cap unless very wide, will reduce the power that can be used when transmitting.
This is due to the antenna length will barely be 3/8th's wave long overall and a closed loop at that.
Square Quad loop is 1005/27.4 = 36.7 ft overall...close to 110 inches each side.
The size frame your using will only give you roughly 14 ft. overall which is aprox. 62% smaller.
http://www.iw5edi.com/wp-content/uploads/2012/07/pfeiffer-quad-antenna-system-reduced.pdf
Above this maybe another option to look at.
GL Have fun
All the Best
Gary