Go with the power strip inside the cab, a lot of MAME builders do the same thing.
The transformer in the bottom of the cab is an isolation transformer, and your old arcade monitor required it. Your VGA monitor has one built in, so it can be plugged directly into an outlet. The easiest way is to just use the power strip, and resist the temptation to wire the monitor power cable into the power supply for the cab.
You'll also need an outlet for the power supply of your VGA converter board, so using a power strip will give you somewhere to plug that into as well.