Niels, I am not sure if I understood what you actually did.
Did updateniceurls.php come up with any errors?
You do not have to edit Global URL aliases or Nodes' URL aliases by hand just to create those URL aliases that worked in 3.9. The updateniceurls script should do that for you. 3.10 just offers the possibility to add nice URLs (in multiple languages) manually if those generated from the objects' title are not sufficient.
Try to rerun
php bin/php/updateniceurls.php
and check the database tables ezurlalias and ezurlalias_ml. And don't forget to clear the caches. ;-)
I had the same problem because I specified a different var directory for each siteaccess in site.ini.append.php and when I use ezcache.php it only clear the cache for the default one... Make sure you clear the cache for all siteaccesses... See http://pwet.fr/blog/url_aliases_transformed_into_numbers_when_upgrading_to_ez_publish_3_10_0
I managed to make a flawless upgrade by running the 3.10 installer with a 'blank' database, dump my old database into it afterward, and then run the upgrade scripts on that.