Depending on your methods, 3D or 3H are typically not forcing.  A 3S cue bid tends to deny a spade stopper, but could be clarified later.  Exploring slam possibilities requires going past 3NT.  This may not be a problem because you can likely make 4NT or better.  However, you may find it difficult to stop at 4NT or 5NT.  

The pragmatic recommendation is to bid 3NT.  You can make 6NT if played by East as the cards lie.  Looking just at the E-W hands, 6NT by East will make anytime the ace of diamonds is onside or the jack of clubs drops.  6NT by West can be set with a diamond lead when the ace is behind the king.  

It would be nice to get to 6NT on this hand.  However, the 1S overcall jams up the auction quite a bit.  How many pairs are likely to bid this slam?  In Wednesday's game, no one bid the slam.

This hand illustrates the value of jamming opponent's auctions.  It also is an example of considering how you will gain the information you need to determine if there is a slam and how you will stop if there isn't before you launch a slam investigation above what is likely to be the field contract.