First off, lets make sure exactly what you are meaning by "hot wire type" gauge. "Hot wire" refers to a large class of different gauge types that rely on thermal transfer to measure low pressures.
If you are meaning a Convectron gauge then the gauge is suitable. If you are meaning a T/C or Pirani gauge then those gages won't work well above about 2 torr and are very dependent on gas mix, and the Pirani gauge won't start working until just before you reach your final pressure. As long as you understand that and don't care if the gauge tells you the truth between 760 torr and 2 torr then they will be suitable. If you are meaning a hot cathode type ion gauge then you are no were near the vacuum level where such a gage can begin to operate, most of them aren't suitable for use at pressures above 10 millitorr.
Hot wire type gauges are very non-linear and sensitive to gas type and contamination. They are difficult to scale. If your control net gauge has on board scaling then count yourself as lucky - those are relatively new to the vacuum instrumentation world.
None of these gauges respond rapidly, so hitting your sixty second mark is going to be very very difficult.
If you haven't yet purchased the gauge then I suggest you seriously consider a capacitance manometer. They are linear, gas independent, less susceptible to contamination, and are well suited to your pressure range. Capacitance manomneters also respond a lot faster than hot wire gauges. They are available with analog outputs as well as device net and control net.
Next, it is very difficult to control vacuum. Gas wets the inside surfaces of a chamber and clings to it, much like water clings to a surface. All surfaces in a chamber will outgas, so even after you reach 200 millitorr and close up all valves, chamber pressure will increase, even in a perfect world where there are no leaks. The outgassing rate can be affected by many things, including how long the chamber has been at atmospheric pressure since it was last used. Outgassing will have a large effect on your ability to control your vacuum level.
If you use a modulating valve then you have to consider how gas flows at low pressures. At 200 millitorr your pump can no longer "suck" gas out of the chamber (actually the pump doesn't suck anything but that's beyond the scope of this post). Before you reach that pressure the flow will have transitioned to a gas flow state known as molecular flow, and the only gas the pump can remove are those molecules that happen to wander deep enough into the pump foreline that the probability of it bouncing back out becomes very low. What this means is that even slight changes to the valve position have huge effects on pumping speed - making control with a PID difficult (not impossible).
Solenoid operated diaphragm valves have difficulty operating at very low pressure levels because the pressure differential across the diaphragm cannot generate enough force to lift the diaphragm and the valve closes under its own weight. Mounting it upside down can help, but then the diaphragm won't close off well at high vacuum levels. Its best to just stay away from them.
You can use a butterfly valve and modulate the valve position but expect a lot of difficulty tuning it, they don't behave under molecular flow the say way they behave they intuitively behave at higher pressures. Under molecular flow you can think of the butterfly valve as a mirror - close it even slightly and it will reflect molecular flow back into the chamber. Without a dense moving gas flow past the butterfly there is nothing to entrain gas molecules that hit the butterfly and carry them into the foreline, so they bounces back into the chamber like billiard balls.
Vacuum gate valves, ball valves, and piston valves usually don't modulate position, they are either fully open or fully closed.
The most common way I've seen is to introduce a inert sweep gas and control pressure by modulating gas in-flow. That's how we do it on our vacuum furnaces. But since you say you can't introduce a sweep gas your best chance for success may be in using two piston type valves (air operated), a large one for roughing and a fine one that is modulated on/off. As chamber pressure approaches 500 millitorr drop out the large valve, then toggle the smaller valve on/off. You may need to play with the size on an inline orifice in front of the smaller valve. At first while out-gassing the valve will need to operate on/off somewhat frequently. As time goes on it will need to operate less often. Given that your gage is accurate to only 2.5% you'll probably have better control potential than what you are measuring anyways.
You can find vacuum valves at
http://www.lesker.com/newweb/menu_valves.cfm
It goes without saying that any leak will render your system uncontrollable, and it can be surprisingly difficult to find and fix some very small vacuum leaks. We cheat and use helium and a mass spectrometer. Since that is out of the question for most you need to be very careful about assembly.
