You ought to be able to smog with two monitors still running. There are 10 or 12 monitors, and you can smog without all of them being completed. Certainly you can smog with one still running, but I'm pretty sure you can smog with two of them going.
The monitors take a certain number of drive cycles, where the drive cycle is specifically defined as lasting for time, distance, and speeds. You do not do a drive cycle just by starting the car and taking a trip down to the corner store for another 6-pack, you have to get on the highway and attain speed for time, then the car has to be stopped (parked) for time and then started again. The point is, if your trips are short and slow then you might not complete a specified drive cycle that completes the monitors.
The point of the monitors is that you cannot reset the Check Engine light in the parking lot of the smog station, then go inside and arrange for a smog check -- you must drive the car long enough for the monitors to go away. Again, you can have two of them running because if they still had trouble after the other 8 or 10 are resetting, they would have reported it by now.
I think somebody is yanking your leg. In Calif., we have the Bureau of Automotive Repairs. You can call them and they will tell you if you are allowed monitors to still be running, and how many. I think the smog shop is in error and they should be testing yoru car for the fees you have already paid. I once removed a carburator and replaced it with a fuel injection system that is CARB approved, and the smog shop screwed up the test and I failed. Basically, he told the machine that the car was modified and this set off the red light with FAILURE blaring from the megaphone. What he should have done is looked that the required parts were removed and different required parts were installed -- the visual portion of the test -- and then tested as a '94 engine instead of an '81 engine. I called the BAR and he helped me get this straightened out. I also have a '94 (different car than above) that failed, and the guy from the BAR said that the car was not tested properly. The shop agreed that the BAR was telling me the right stuff, and that they did the test differently, so they tested again and the car passed. Barely, but it passed.