You have in 'Seth's' the juxtaposition of two syllable-final fricatives: /th/ and /s/, which English abhors, pronunciation-wise. What happens is that the first fricative is elided in normal speech, giving us something like /ses/, except that the tongue will still make a movement towards making the /th/, thereby (perhaps) slightly lengthening the vowel. Similar examples are: 'clothes, loathes, deaths, sixths, strengths, tastes', and so on.
Iconoclast: maybe there's regional variation? I think I would always pronounce the the 'th' or /θ/ in Seth's - and this might be partly because it's a name. I agree with you absolutely about the lengthening though. When singing, it's a bit of a problem because you want to minimise the length of the consonants. Some of the words you mentioned also have standardly acceptable variant pronunciations:
clothes - /kləʊz/ (rather than /kləʊðz/)- this pronunciation is indicated in some dictionaries
strengths - /strenθs/ (rather than /streŋθs/) - also indicated in some dictionaries