Who is paying for a broken window.
I would not consider a digger anything like gentle enough.
Use the digger for what it’s for, dig out that soft ground and replace with type 1.
a few grands worth of glass is not something to mess with.
what do they weigh out of interest.
my 4.8m sliders we lifted in with 5 blokes and suction cups.
having now done some sums your 2.6 x3m is 7.8m of glass.
my 4.8 x2.1 is 10.08 of glass so they could well be liftable by hand.
depends how high they need to go, we had to lift from a pallet crate up 300mm onto the door step, i would not have wanted to lift them 750mm high or more, I think if I did I would have used the telehandler and suction cup frame that you can hire.
our window company quoted to use a glazing robot, I declined and said I would lift them myself, when the fitters turned up I asked them about the robot and they said they prefer to pick them up by hand.