Sounds good Attilio - you've got enough tracking range so far. It would be good to check the XO stability just to make sure, before doing anything to the 7L13. While you have it all warmed up, monitor the XO tune (tracking) voltage on a scope, and run the tracking control all around, and especially near where the peak response shows on the 7L13, set for the 30 Hz IFBW. Make sure it stays at a steady, but variable (set by the tracking pot) DC level, with no signs of jumping or oscillation in the loop.
To adjust the 7L13, the whole thing should be in the manual. You shouldn't need the TG for this, but you may need other equipment. To do a whole calibration, it may be quite tedious, but if you were going to anyway, this might be the right time. You may be able to just do the IF filters for now, just to see if it will work well with the TG. You'll have to read up on everything in the manual, and figure it out. Good luck.
Ed
