pictures? can go a long ways in help explaining things.
with you putting in a french drain, i am going to assume you are working on the dam side of the lake. and at the bottom of the hill/dam, and it is a wet soggy mess down there.
if this is the case... i think this be one bad year to try and get into those areas. due to amount of rain. at least here has been a lot.
if you can wait say in "fall" or "winter" when things dry up some, you might be able to get in there better, if you can wait till more of a drought year, you will have much better luck.
a tracked unit, will more likely hold up better in soggy conditions within reason. example a "mini ex" mini excavator / track unit that you could rent (equipment rental in the old paper phone book) with excavator / track unit, you can build "old lumber rafts" per say. and use excavator to move them around. to act like large pieces of plywood to get you through the mess. ((see various youtube videos out there))
just glancing at google for "JCB MIDI CX" looks to be an industrial tractor, and going to assume R4 / industrial tires on it. your going to be in some pain. with the fat / wide tires, you will be slipping and sliding and being stuck. and working the FEL (front end loader) and the backhoe like an octopus to drag/push your way through things only making a mess. if ya had R1 / agirculture tires on machine 4x4 / MFWD i might be tempted to try, even if it resulted in making a big mess or getting stuck *that's just me though*
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with above if you can wait till more of a drought year, or portion of the year were everything is just more dry. you will most likely have a much better install and less complaining exception muscle aches don't count