Have you taken any steps to put your plant on the path to rejuvenation? Timing of the work is an important factor, with winter being the worst time to undertake any significant work like heavy pruning or a full repot. I've don a lot of rejuvenation work on old indoor trees like schefflera and many species of ficus, citrus, others ...... if you want to make a plan that takes into consideration the plant's natural rhythms and strengths while making allowances for the parts of the growth cycle when the plant won't be as strong.
(1) Can I cut back severely (well below any leaf nodes) and expect new growth and branching to occur? I've marked hypothetical cut marks in yellow in the image below. You can cut schefflera back very hard, but the enthusiasm with which the plant responds will be based on several factors, the major considerations being: 1) The plant's current state of vitality (health). 2) Timing. By far, the best time to repot (unless you live close to the equator) is in the weeks just before the summer solstice. Reason: The plant should have as much energy in reserve as it is capable of saving (given its stress level), and it's current ability to make energy/ food will be about to peak. This means more enthusiastic back-budding and a much faster recovery. Recovery from heavy work in the winter can take months, during which the plant will be more vulnerable to insect herbivory and disease pathogens.
(2) If yes, any recommendations on how quickly I could cut back the main stems? I was thinking one to two major cuts every year over three to five years. It's best to do the hard pruning all at once. Here is a typical repotting sequence:
(3) I need to re-pot/re-soil the plant. Should that happen before, after, or at the same time as the pruning to avoid undue stress? While the hard pruning should be done all at the same time, you'll get the best results if you repot in June (if you live in the US), then give the tree a year to recover and build strength.
Al