Sometimes, the Snap tool is not enough or can be quite difficult to use because of a particular shape of the high resolution mesh; in these cases, the Shrinkwrap modifier can be very handy.
Basically, the usage of this method is all in the preparation of the modifier:
Assign the Shrinkwrap modifier to the Gidiosaurus_lowres mesh and, in the modifier stack, move it before the Subdivision Surface modifier.
Click on the Target field to select the Gidiosaurus mesh item and leave the Mode option to Nearest Surface Point (this seems to be the more efficient mode for this task; by the way, you can experiment with the other two modes that can reveal themselves useful in other situations).
Enable the Display modifier in Edit mode and Adjust edit cage to modifier result buttons (the penultimate one and the last one to the right, with the cube and four selected vertices image and with the upside-down triangle and three vertices image...