On 3 different cars I have used the same tools...

I have a piece of 2x2 box tubing that sets under the frame rails just below where the radiator bolts in...

It has a chain attached that runs up to my cherry picker...

I have never removed grills...bumpers...hood or anything to change engines...just the radiator...

The dolly I use sets on the oil pan rail of the engine...I set the engine down on the dolly with the dolly close to the rear of the engine...

Then I put the transmission...starter...headers...trans mount and everything else on...

I put the K frame and steering box on and then install the lower control arms and strut rods...

Once everything I want is bolted on I lift the car up and wheel the dolly into place...

I keep my back tires on the ground because the dolly I use is short but some others do lift the back tires...

Lower the car down slowly until the transmission crossmember will bolt in with the 4 bolts...

I leave the transmission mount loose on the trans and on the crossmember until after I have installed the 4 bolts for the K frame...

Lower the car on down until the 4 K frame bolts can be installed...

Once they're tight I raise the car back up and put it on jack stands to finish everything underneath...

The whole process from the time you lift the car until everything is setting on the stands is about a half an hour...

The below pics are an install on Dads 72 Duster...