Personally I'd stick the extra flap in and possibly S turn. Not because I'm afraid of slipping; in a warrior I regularly sideslip - it's effective, and I'm comfortable with it, but the warrior doesn't have a limitation enshrined in the POH.
I have been lead to believe that the restriction noted in the 172 POH is because in the earlier days, a few suffered a full tail stall when so doing, and promptly nosed over completely - i.e. the flow over the tail can be sufficiently disturbed to cause a tail stall, not just a loss of effectiveness. I don't have a verifiable source for that though.
However, the 172 example I fly goes to 40degree flap, whereas yours seems to have 30 (later model). Both contain the same verbage about full flap slips not being advisable/permitted:
If I reduce to 30deg (less than full flap), can I slip where you can't? I doubt that..
Is the warning not necessary for yours? Maybe.
Where's the limit at which you can slip? Dunno...
So that's why I'd not slip - it's quite possibly corporate a$$ covering, but I'm not wagering my life on that - I'll avoid slips with flap extended in the 172 period. That said, every crosswind landing ends with a cross controlled, wing down arrival.. which looks remarkably like a sideslip
P.S. S turning shouldn't require much calculation - you're already well above Vs, just let the nose drop a bit in the turn, allow it to gain 5 kts or so, and don't go nuts with 60degree banks..