The Elliott 10M is from memory approx 400kg got mine onto the trailer for the 120 mile journey home with an engine hoist and some 3/4" nylon rope.
At the other end I used my "Shaper Shifter" which is a home made weldment of steel pipes approx 6' tall and 28" wide this is set up with 2 pulleys to use an M-Mart ratchet to lift the Shaper, once lifted above 8" two timbers are inserted into the bottom of the device and the shaper lowered onto these thus removing the chance of it pendulum-ing. As its on H/D castors it's then simply a case of wheeling it around like a top heavy trolley.
The Elliott is very top heavy and the "pendulum effect" when using an engine hoist can be enough to topple one over. if I might suggest that once raised you put a couple of stout planks/timbers across the legs of the hoist and lower (at least some) of the machines weight onto these.
As to using wire strops this may damage the machines working surfaces, when slinging an Elliott 10M its done using the ram, from memory I think the Elliott book even shows rope being used.
Regards
Paul