Astrometrica will work for stacking but you will need to enter the offsets manually since the internal ephemeris generator doesn’t work for significantly hyperbolic orbits. I’m hoping Herbert Raab will get that fixed sometime.
It has been interesting to see how many common programs can’t cope with e=6. This will be a good opportunity to get them fixed! I use my own code for stacking and it uses the Laguerre algorithm for solving Kepler’s equation to find the eccentric anomaly as documented by Bruce Conway in 1986 here:
https://adsabs.harvard.edu/full/1986CeMec..39..199C
It is very fast and appears to be stable at least up to the eccentricity of 3I/ATLAS.