I haven't tried it, but I expect you could cat your drive to a file, put the file onto the bootable DVD, boot off the DVD and then cat the file back onto a replacement hard drive (of equal or larger size). Probably some way to pipe the file into tar format as you proposed above. I fully expect it would work if you can work out the syntax.
My means was to done this automagicaly, for a non tech user. I think doing it could be not so difficultly done by doing a bootable dvd with minimal system with the inittab that run a script dd'ing the image, but I was thinking one tool already exits for this purpose... Once I have a couple of free days i'll try it... in 2025...