To reply to my own questions:
I managed to get the goop off quite reliably by scraping it with a hard plastic chisel like thing. I think I got this once with an old ipod replacement battery. It was meant to pry off the screen. I think a sharpened guitar pick may also do. The silkscreen confirmed that they are NTC's.
I found the NTC which I completely cut off (NTC2) in my trash, which is very lucky, because I completely destroyed NTC4 when desoldering it from the board. I think the other side of the leg was still embedded in goop. So I measured NTC1 and NTC3 while they were still in the circuit. To caclulate the Beta I tried heating them up and measuring their real temperature with a thermocouple. Unsurprisingly these measurements were garbage, due to the rest of the circuit, and differences in thermal mass connected to the thermocoule and the NTCs. The only thing I could see is that the 2 NTC's were identical.
To eliminate the rest of the circuit, I glued the legless NTC2 to a piece of nickel strip, and managed to solder some wires to it. Then I could heat it using a soldering iron on the nickel strip, without fearing to damage the BMS more. This gave me measurements which were slightly good enough to have a hunch that it is a 10K NTC with a 3950 Beta. So I splurged on Ebay to buy 10 of them.
I glued 2 of them next to my poor NTC2:
When heating this, the thermal coefficients couldn't be more clearly the same.
So now I'll continue to remove some more goop from the board, and populate NTC2 and NTC4 with my new ebay stock. I think there are 2 groups of 2 NTCs because there seem to be 2 separate controllers on this BMS. Could it be that each of them is responsible for 5 cell pairs, and measure temperatures independently from each other? So Placing one NTC from controller one close together to one of the NTCs of controller 2 would make them trigger fire mode at about the same time?