One thing about panspermia math: why assume current travel conditions between the stars?
Today the Sun is very far from other stars, but early in star formation (within nebula) the stars are
1. much closer together
2. have a higher rate of material ejection (mass exchange)
3. likely have more benign radiation environments unless near a star, due to GCR shielding by nebula gas
4. likely have higher equilibrium temperature in interstellar/interplanetary space
Combined, these factors yield orders of magnitude improvement in panspermia efficiency vs the Sun.
Yes indeed, I've thought panspermia in the Sun's natal cluster is an interesting idea. What could make it even more interesting is that small bodies in our Solar System (and likely its sister systems) were warm enough for liquid water to exist for some millions of years then, so there would be an enormous volume of material in which Origin of Life might have occurred (and, if it did, to then spread after the parent body froze and then fragmented.)
It would make a fine science fictional scenario that could get around the Fermi problem: those 10,000 or so systems could have life, but the rest of the universe not have life.
This has occurred to people! But if you run the numbers, they are still not good enough in that early (~100 My) window when stars in the parent nebula are close together, you get something like 1 chance in 1000 of possible panspermia events (based on modeling lumps of rock flying back and forth). Not terrible odds, but nothing like the Mars -> Earth odds.