My pleasure Carrie and yes transcribing the β (in the Netherlands we call it the Ringel s) as 'ss' (or 'sz' ) is correct. This was or is done when the ability to produce an β is not available, for example, on older typewriters or in domain names on the internet, one writes ss. In the past they also used the sz (es-tset). But if it's possible the most correct way to use, write or type it, of course would be Janβ.
But on the internet/online archives and for us also I think, transcribing it as ss (or sz) probably is still done and works better, because it would make them much easier to find in a search and could prevent new duplicates ?
Transcribing Janβ as Janssen is a bit tricky, it might be correct, if you transcribe or would like to write them all with the full meaning of the abbreviated endings of the patronymics perhaps, but it would be a bit the same as saying we now are going to change for example how we are writing or using all patronymics with the abbreviated endings, like Jansz, Jans, Jansdr and we now are going to write those with the full meanings, it sounds or looks easy perhaps, but it would create a whole lot of new and even more problems, because it would depend on the time and the place if the full meaning of the abbreviation or the ending of the patronymic was Janssoen, Janssoon or maybe Janssen, or perhaps even Janssone and so on.
If we go even further back in time, they would for example write patronymics or names like this: Jan Heer Janssoen or Jan Heer Jansone (translates as Jan lord Janssoen /soon/sone and they all mean= Jan son of lord Jan) (in the middle ages they often wrote the full words for son or daughter the spelling could variate of course, so it could be soen, sone, soon, doghter, dochter)
So I would not transcribe or change the patronymics to the longer versions if the original records only show the ones with the abbreviated endings. You can transcribe the example to Janss or perhaps even Jansz, to make sure they are easy to find and to prevent duplicates, but the abbreviated ending in Janss could mean Janssoen, Janssoon, Janssone or Janssen so there would be several options and either one might be correct for that time and place, it would not make things easier. ;)