(To extend to a third case, in 'These pills do help' the /s/* is realized as [z]. This is the case you speculate about in your last sentence - you're not alone in this voicing!)
PS Lots of slips; I've left them for the record, but here are the corrections:
* It's /z/
** pre of course, not inter-.*****
*** Because it was /z/ in the first place, nothing surprising happens here. It makes a [z] sound.
**** Because of the first correction, it doesn't have any voicelessness to retain.
So many slips Sorry if I've misled you BC!
PSS *****Except in some dialects, where the /l/ is vocalized - for example http://en.wikipedia.org/wiki/Estuary_English#Features . Then it is intervocalic.