In Jewelry work it sometimes helps to have a hot plate. It might also help to have a heat gun to keep the work warm. Some multimeters have a thermocouple input. If you are worried about burning the chip stick it onto the center of the package. I do not know if this would work in or not.
Jewelers also use silver solders and torches, the process is the same.
You might try clamping the parts with the holes between sheets of metal to act as a heat sync. Acetone will dissolve this. Use Alcohol to clean the excess flux from the board. It is easier to add solder than to remove it. As for the micro-machining it takes specialized equipment.