Solution #1: Get a jog dial.
Shown on the right is a Z-Bot Jog Dial II from Little Machine Shop (US$89.99). It is a USB device, and comes with a disk which installs a plugin to Mach 3 allowing the jog dial to jog the axes.
Pressing any of the buttons once switches the dial to control that axis. The middle dial "clicks" when turning, and each click steps the axis once. I'm not sure if there is a setting for how much the axis steps, but mine stepped 0.001 inches per click.
The ring around the central dial is spring-loaded, and lets you move the axes at any of several speeds. The farther you turn the ring, the faster it goes.
Even after fooling with the thing for a few minutes, I realized how indispensable this will be.
Solution #2: Make your own vise clamps.
But not the ones from Little Machine Shop, which proved beyond my ability due to the need to drill 3/8" holes through an inch of steel. Instead, follow this Instructable by Doc Workingday.
All you need is 2" x 0.25" angle iron (he used a scrap piece, I was forced to buy a short length of weldable steel angle from Home Depot: US$15.95) and a bit of 3/8" threaded rod (I could have used a piece from my clamping kit, but instead I got a short length of it from Home Depot: US$1.24).
Rather than using a table saw or a hand saw, I'm planning on using a metal-cutting abrasive cut-off disk on an angle grinder. I wonder whether the steel will be cut through before the cut-off disk ablates away to nothing...