You shouldn't have any problem at all. My Ezgo TXT with 5" lift and 23" tires measures 75" tall and fits just fine with maybe a little more than 2" to spare. I'm Fuzion and not Grand Design, but the Happi-Jack beds seem to be mounted the same in all of the toy haulers. Based on the measurements provided previously, it sounds like the 355 has the same clearance as my Fuzion 315.
As mentioned previously, letting air out of the tires can gain you maybe 2", but that can be a real PITA. XT-Innovations has a hinged bracket system that allows you lower the roof close to 3" by just pulling a few pins.
XT-InnovationsEither way, you should have no problem at all with a 4" lift and tires no larger than 23". I wouldn't lose any sleep over it!