Cells are possibly running very hot, maybe plastics / tapes / whatever around them are giving the smell. The 18650 cells Dyson uses definitely will have some passive safety built-in, but it's not a good idea to rely only on that. 18650 PTC cap tends to trigger around roughly 100degC surface temperature.
What could the BMS do? You have not added temperature sensing to the cells, after all.
Second-life use is always problematic, but it's especially problematic for relatively large discharge currents, because aging mechanisms usually hit the internal equivalent DC resistance more than it hits the capacity. For example, End-Of-Life is often defined as 30% capacity drop, or 100% DC resistance increase, whichever comes first. Old cells that have half the capacity left may easily have 2-3 times the DC resistance. In other words, the fact a vacuum cleaner is only running for say 6 minutes instead of 60, does not mean there is 10% of capacity left; it can also mean internal DC resistance is so high that low-voltage cutoff limit is met after discharging only 20% of the capacity or so, because of the U = R*I drop of the cell! But these cells could perform just fine in low-current application.
Therefore, I would not try to use aged cells for loads that need more than say 0.2C average current or 0.5C peak current.
"Small old pack is fine because I only make short trips" is actually the worst case, because that implies high current relative to the battery capacity.
And, of course, I cannot recommend doing any of this at all, so always remember there is a risk involved.