We are also talking about the draconian rules they impose at the Silver Kris lounge and 'by the book'.

I think it might be easier asking for your hotel for early check-in than getting a shower at SQ lounge. Your luggage will be at the belt by the time you reach immigration!

However, do tell SQ ground services that that is what you intend to do first. Otherwise you might find your bags at the lost and found counter instead!