I just went out and practiced on Sophie, she had pretty regular vet visits now but can't get herself into the back of the car anymore so we lift.
I don't do the basket hold, she's 36kg but quiet light for her size (was well over 42kg when she was younger)
To lift her in I put her front legs up then lift in her back end.
To get her out I hold her in front of her front legs, she has a big chest so the pressure isn't really on her neck and my other hand goes in front of her back legs.
She's quiet top heavy so lifting her in the basket way probbly wouldn't work aswell, her front end is huge compared to her back end and it would over balance her.
And when I put her down, she relaly needs to land on all 4 feet to keep herself up, If I bent her legs up she'd stumble around trying to get her footing everytime.
Buster I pick up using the basket method though, he's only 21kg and still fit and helhty though.