One of the interesting things in that Wikipedia link is that you only need to run your Orion for 36 days to get it up to speed. Beyond that, detonating more bombs won't accelerate you any further.
So yes, you could turn it around. But surprisingly it seems you can wait until a month before arrival to do so. The downside, however, is that your max velocity gets cut in half if you bring enough bombs to slow down.
With better explosives, you could get a higher max velocity and therefore closer to the "accelerate halfway, decelerate halfway" ideal case, but at the moment such explosives don't exist.
Do 36 days of acceleration at the beginning (or spread it over a year to reduce peak acceleration) -- go from 0 to 0.1c or whatever the cruise speed is.
Coast for ~100 years.
Spend the last year going from 0.1c to 0.
It does mean you have to carry twice as many bombs, and carry half of the bombs for 149 years, but bombs are really lightweight relative to the ship. It also means you can't just jettison the pusher plate, which is probably a bigger deal.
In this case, the weight of the bombs is larger than the rest of the ship: 50K tons for the ship structure, 300K for the weight of the bombs [1]. Twice as many bombs essentially doubles launch mass.
Orion is a great concept for tooling around the solar system easily, but what it buys us over interstellar distances is that it makes macroscopic payloads and reasonable travel times possible; they're still not easy.
Just to reinforce: Orion is still a rocket. And not a particularly efficient rocket, either. It uses an incredibly energy-dense fuel, but not so dense to allow you to ignore the rocket equation.
It's not twice as many bombs, it is (using your numbers) six time as much bomb mass as payload mass, so 50Kt payload, 300Kt bombs for slowing down, which gives you 350Kt payload for the acceleration phase, which would require another 2100Kt of bombs to get up to speed, for effectivley seven times the launch mass
I wonder if Elon Musk has ever spoken about Orion.
I'd love to live in a world in 2030 or so where a private shuttle runs Earth-Mars every few weeks using Orion technology, since it wouldn't then need to operate on energy-conserving orbits.
Sure, but it raises the number of nukes needed at launch considerably, holding the travel time constant. More than double, even leaving aside considerations like the additional storage size.
Also, designing nukes that last for 150 years before being used is non-trivial (can't use tritium in the initiator, for example; it decays too rapidly for that).
