Here's the thing. When you add motion to combat, you introduce a set of variables that are hard to control and that make the whole process even more complex.
But you have a great idea. I would limit the possibilities for moving. You don't want members of your party getting far away from each other. You don't want characters abusing your rules or getting abused by unforeseen consequences.
For this to work, both sides need goals of some kind. Vader wanted to recruit Luke, not kill him. Luke wanted to kill Vader, but that goal quickly changed to escape. Goals give you a narrative, and a narrative gives characters reasons to move.
Here's a proposed, untested rule for handling combat movement. If there's something similar out there, well, great minds think alike.
Some may complain that this rule hurts player agency. If the alternative is certain death, I'll take the humiliation. Keep in mind that this rule should be used sparingly.
The Harry & Parry Rule
Prerequisites: The DM must approve each use of this rule, mainly to avoid abuse. Reasons to disallow include two combatants who are evenly matched, a defender who's avoiding combat unnecessarily, a defender who can't retreat, a tight schedule, and lack of a clear goal for the attacker. Reasons to allow include an attacker backed into a corner, an attacker who needs to reach a location, and a defender who would otherwise be killed.
First, a character must declare that he will use the rule in a given round. The rule remains in effect during the round unless it becomes irrelevant, e.g. opponent is killed. The character must take the role of attacker or defender, which forces his enemy into the opposite role.
Second, the attacker makes a normal attack, with all applicable modifiers. Damage is calculated normally but not applied. The attacker is harrying, which involves footwork, taunts, brute force, and intimidation, as well as the usual weapon skills. The defender is parrying, with every move devoted to avoiding the onslaught.
Third, compare the damage total to the defender's Stability Rating. (This is the untested part.) The Stability Rating could be the defender's level multiplied by some constant. It's a measure of how hard it is to make the character move. If the damage equals or exceeds this number, the defender must retreat one space. If the damage is twice this number, the defender must retreat two spaces, and so on. The defender chooses which direction to move. The attacker has the option to follow. If the damage is less than the Stability Rating, there is no effect.
Fourth, the defender makes a dexterity check (assuming he had to retreat). If he fails, he is considered off balance. At this point the attacker may take a single action to accomplish his goal. If the terrain allows, he may push/trip the defender. On a sloped or uneven surface, the defender will fall, with the obvious consequences. At the edge of a drop, the defender gets a saving throw, with success meaning he falls but grabs the edge.
An attacker may continue to Harry for any number of rounds. A defender who is off balance will continue to be off balance, with a penalty to his Stability Rating. The defender may regain his balance by passing the dexterity check, although he still must retreat. The attacker or the defender may call off the action at the end of any round and resume normal combat.
The defender and the attacker take no damage from the Harry, representing the attacker's superior skill. They may, of course, take damage from falls, spells, attacks by other combatants, and other dangers.