In all probability the 162V was somewhere near accurate because the capacitor is charging up to the peak of the rectified DC and there is no load other than your meter to discharge it. So the meter effectively reads the peak voltage.
If you take the capacitor out, the voltage will be as swgrmfg said, save for a small error caused because real-world diodes have a small but finite forward volt-drop. So instead of 108V average DC you might have 106V average.
You are seeing the old problem of an averaging meter which is scaled in RMS, or perhaps even a true RMS reading meter being used in an application where an average reading instrument is required. Most college level electrical principles books have a decent chapter on the mathematics behind the different measurements - it might be worth having a look in your local bookstore or in the library.
The following link might be useful - I haven't read it in detail, but it seems ok on a brief skim through.
One possibility for your overspeed condition is that you are running with a slightly weak field, at about 90% of rated current. This, counter-intuitively, causes the motor to run faster. It is a technique known as field weakening. The motor will also be have a rated speed quoted at rated power. The speed will rise off-load.
If you can provide some smoothing capacitance, the DC will have less ripple. This is a good thing. Instinctively I doubt 1000uF will be enough to produce a smooth DC, but it is a start. From the smoothed DC supply you could then use one resistor in series with the field to set the field current to its rated value, and a separate resistor in series with the armature to set the speed to your desired value. This should give better results than simply dropping the combined field and armature voltage through one resistor.
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I don't suffer from insanity. I enjoy it...