No, sorry. At this time it is simply not possible to do. The problem lies in the fact that fantastico is simply a third-party add-on for cPanel, the control panel that is running on server 1 instead of directadmin, as is on server 2. Fantastico, being as add-ons tend to be, cannot run unattached to cPanel.
I definitely understand the attractiveness of Fantastico, but in my eyes it shouldn't be too large of a problem for anyone. All of the most popular scripts now-a-days make it insanely easy to install themselves. It's usually just a process of uploading, CHMODing (only sometimes needs to be done), and running an install script. The entire process should take under 10 minutes or so, depending on how quickly your Internet connection can upload.
Last, but not least, we are sorry that we can't accommodate this need of yours. Please feel free to post any questions that you may have about installing scripts or anything else and you should have a sufficient answer in no time at all.