Yes you can use a DBS LNB to find Nimiq 1 and then swap to a Ku and you should be in the ballpark with Galaxy 11. I say "in the ballpark" because the signal on Nimiq 1 is much stronger and the dish may have to be further fine-tuned to bring in Galaxy 11 perfectly. Remember to set your L.O. (or Local Oscillator or LNB freq) to 11250 when using the DBS LNB and set it back to 10750 (or 9750/10600 if you have a universal LNB) when you swap it for the Ku LNB.
As far as an active transponder, I'm not by my system at the moment, but G-11 is mostly feeds so they come and go. You could try 12060 (V), SR 26700, FEC 3/4 which, according to lyngsat.com, is Trinity Learning and there's a free channel there. Maybe someone else will chime in with another active transponder.