Technically, Singapore is a One-Stop-Security country. Unfortunately no one knows why Singapore Airlines dumps their passengers most of the time into the unclean area.
If the agent in Singapore agrees on checking your baggage through you will most likely be fine (as you'd only have to pass Security).
If they don't, then it will most likely work out as well (you'd still have 2+hrs to collect your bags (most of the time they dispense the last bag after around 90minutes)), but is more on the risky side because of immigration and baggage dispensing.
As they will most likely load the containers in Singapore the right way, your bags should be amongst the first ones to get dispensed (if FRA unloads them in the right order).

ZRH seems to be already starting some pilots regarding the kiosks, but I haven't heard anything about FRA yet, though.
If they would already start with it, the kiosks will only matter if you'd have to go downstairs to collect your bag to recheck it.