Upgrading large website from 4.6.8 with several modules

Hi all,

I love Drupal. From the very first time. I think that it's an excellent CMS, easy, powerful, flexible, etc. etc. etc.
But... if you have to update it, it can be absolutely CRAZY!
Let me explain my case:

My website runs Drupal 4.6.8 (yeah, pretty old...), and it has several add-on modules included - being the most important ones "image" and "img_assist". I found them to be very useful for that early Drupal version, but now I guess that they are more annoying than useful...
I also have some "listhandler", "mailhandler" and "userspoints", but those are not that crucial.

My site has, as reported by MySQL, 320 users, 469 nodes, 566 comments, 66 images... and I will obviously *not* enter all those by hand in a new Drupal installation.
Unfortunately, the 'update' scripts do not work very well... I've been able to update the site fairly OK to 4.6.11 (the last 4.6.x series I think), but beyond that nothing works.

I've tried (some examples):
- with all possible modules deactivated
- with the standard theme (Bluemarine) activated (which, BTW, is not working well in my installation!)
- copying the new drupal files over the folder, or starting from scratch
- etc.

...and this, for updating to 4.7.11 and to 5.7. Updating to 6.1 directly obviously doesn't work neither. I've always followed the guide.
Fortunately I have a "mirror" of the site where I can do the many tests.

As an example, in the update to 4.7.11, the Update script reported (even before starting) something like:
Warning: Unknown column 'referer' in 'field list' query: INSERT INTO watchdog (uid, ... in /var/www/.../includes/database.mysql.inc on line 121
...and many other errors after the update.

What could I do? Any suggestions?
Would there be some possibility of starting from scratch, and then using some kind of "DB import utility" to retrieve the old contents, formatting the tables adequately? That would be great!

Many thanks in advance,
Jordi :-)