1) the 'now 2 months' is down from the 'best time of 6 months', caused by mars being literally closer to the earth.
That's not how Hohmann transfers work. Just stop. And a minimum energy transfer to Mars is 9 months anyway, not 6.
In order to achieve the 2 month travel time, it must launch WITHIN THE LAUNCH WINDOW.
Get this through your head: There Are No 'Launch Windows' With Nuclear Propulsion. You don't leave a craft that can travel to Mars a matter of months sitting idle rusting away rather than repeatedly ferrying back and forth, just because some times the trajectory is somewhat longer and others it's somewhat shorter.
There are launch windows with minimum energy Hohmann transfers because that's what you need to have Mars be at the right place when you intersect its orbit. It takes roughly the same amount of energy to intersect Mars's orbit regardless of when you launch a Hohmann transfer, but unless you time it right, Mars won't be there. Launching at any other time requires more dV to dogleg it - and dV is dearly bought when it comes to chemical rockets. It isn't dearly bought with nuclear rockets. So launch windows simply don't apply to them. You launch on an elliptic which doesn't terminate at Mars' orbit, aka you applied more delta-V than was necessary to get out that far, but that's happening by definition if you want to get there faster. A minimum energy elliptic can only intersect Mars orbit opposite its starting position, but the higher the energy of the transfer, the more rotated the interception point is.
I will repeat: your capital cost is in your rocket. You're not going to leave it sitting around waiting for 2 1/2 years when you could do 10-ish trips during that timeperiod, just because some are longer than others and some somewhat shorter, and thus raise your capital cost per kg tenfold. They're all varying degrees of "short", and you have flexibility; you're launching on all of them. Unless you're an utter moron who likes throwing away 10x more capital at a project. You do not have to intersect the planet at a specific location on its orbit in opposition to your starting point when you apply more than the minimum dV.
since the ships ARE NOT THOUSANDS OF KM APART, due to ALL LAUNCHING IN THE SAME WINDOW
Launching just days apart in the same window (which again, THERE ARE NO WINDOWS), they're MILLIONS of kilometers apart. Do you not even know how far Mars and Earth are apart, or can you not divide a travel distance by the number of days of the trip?
And for the last goddamn time, the exhaust doesn't even remotely resemble a collimated beam, even if it did it would still be orders of magnitude weaker than ambient radiation, and even if it wasn't all you had to do was microscopically off-angle it. This is such a stupid line of discussion.