How to display progress bar for tar incremental archives

It shouldn't be very difficult, at least for archives that are compatible with the old-style format where file names are stored in a fixed-size (100 bytes) field, but I don't know of any tool that can rename a file in place in a tar archive. Besides, with a compressed archive, you'd need to create a new file anyway.

It should be even easier, but I don't know of any existing tool that can filter an archive, renaming files as it goes. You can build one on top of tar libraries in scripting languages; for example, here's a proof-of-concept script to rename a directory in a tar archive using Perl with Archive::Tar. The archive is loaded entirely into memory; this is an intrinsic limitation of Archive::Tar.

#!/usr/bin/env perl
## Usage: tar-rename OLDPREFIX NEWPREFIX
use strict;
use warnings;
use Archive::Tar;
my ($from, $to) = @ARGV;
my $tar = Archive::Tar->new(\*STDIN);
foreach my $file ($tar->get_files()) {
    my $name = $file->name;
    $name =~ s~\A\Q$from\E($|/)~$to$1~;
    $file->rename($name) unless $name eq $file->name;
}
$tar->write(\*STDOUT);

GNU tar doesn't have the ability to rename members on the fly, but pax (POSIX's replacement for cpio and tar) does. However, you can't make pax both read and write from an archive. What you can do is expose the archive as a regular tree through AVFS, and create a new archive with pax. This retains file names (except as transformed), contents, times and modes but resets file ownership to you (unless executed as root).

mountavfs
cd "~/.avfs$PWD/old.tgz#"
pax -w -s '!bar!baz!' -s '!bar/!baz/' . | gzip >new.tgz

If you add an extra v to your tar command which writes to the drive, it will report the file sizes; you could perhaps parse that and compare the file sizes, without having to read all the files twice.

You have to realise that this is no substitute for proper verification, and the only real verification of a backup is a restore... Note that LTO drives verify writes as they go, so you're not quite driving blind here. But simply relying on file size comparisons doesn't tell you all that much!

I'd actually strongly recommend using proper backup software, such as Bacula which is ideally suited for tape backups. Once you've set it up, it will take care of your verifications for you.