Welcome to the community! :)
Do not put too much thought into impedance transformation IMO. An 1:1 should suffice if needing additional isolation for common mode, though admittedly I ran my LoG for many years without any balun or transformer. 1:1, 4:1, or whatever else tried when constructed did not affect it much. FWIW, there were just a few relatively useless ferrites on the feedline near the feedpoint.
Your LoG as described should be "resonant" somewhere below 700KHz. Being on ground is going to lower resonant frequency below the usual freespace calculation. LW through MW including 160m should be fine, but getting much above there the signal pattern is going to break into multiple lobes. There are also ground losses to consider.
My comparatively small 148' LoG over lossy ground was resonant somewhat below 7MHz with usable receive performance from LW up to about the 20m band. Above 15MHz usually required a preamp.
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I built my shielded LoG out of cheap RG-6, and it survived many years of use deployed in a moderately wooded area. It is up for repair or replacement now, but seeing as I have yet to examine it, the actually recent failure just as well be a feedline or feedpoint issue instead of the RG-6 loop being damaged. Anyway, here is what I did:
https://www.hfunderground.com/board/index.php/topic,29940.msg114696.html#msg114696BTW, while we often use the term "shielded," most coaxial loop designs are more about potentially improving current balancing versus a single wire. It should not really matter either way assuming good loop symmetry. YMMV.