I do hope you got all the potatoes out, though, Nick, or are prepared to treat potato volunteers either as weeds, or be willing to transplant them early.
I haven't sat down to figure this one out, because honestly, I like to think about garlic as a necessary crop that is also a handy fumigant, as mentioned above. If you disperse your garlic plantings, their fumigant and scent distractant properties benefit everything around them, but it complicates tending and harvest, though not so much if the complimentary plantings are similarly timed.
As to potatoes spreading disease, everything that I have ever read and learned on the matter has
led me to form the strong opinion that that's not quite accurate, or at least not that simple.
Potatoes can have issues with disease, true, and there hasn't been much genetic diversity in potatoes, which means that they all share similar weaknesses, so when one potato catches something, it's unlikely the others will have an immunity. But even if your potatoes were diseased, those diseases would affect solanaceae relatives. So no tomatoes, eggplant, datura, basically no nightshades at all.
But if you get rid of all potentially affected biomass, like the dead plants and leaves, down to the
roots, and if you brew up a good actively aerated
compost extract and treat the area with appropriate fungal slurries, you can build up the good soil life that crowds out and out-competes the pathogens. While this is great for the soil and will let you return to the former crop sooner, all you really need to do is switch to a crop that doesn't host the disease in question, and, like garlic, perhaps has fumigative properties.
Let us know how it goes, though, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein