Well, for some reason my Mavic (.400 firmware, GO4 4.1.0) doesn't behave the way you describe at all.
When I'm in RTH, I can use pitch (Mode 2 right stick forward/back) to speed it up, all the way to 33mph at full stick, without canceling RTH.
I can also change altitude with the left stick, without canceling RTH.
Just did exactly these maneuvers yesterday, precision landed within 2 inches of take-off.
So, somethings different about my Mavic from yours -- radically so.
Further: Turning the controller off to initiate RTH is an exceedingly foolish idea. Perhaps the most important "rule" when flying a remote piloted aircraft:
Do not ever deliberately lose control of the aircraft when you have control; you may not be able to re-establish control
I'm hard-pressed to think of any worse advice than to completely remove your ability to control the drone while in flight. Autonomous control during RTH is not some sort of sophisticated AI that will avoid dropping on someone's head. No, it will drop the drone into a crowd if it hits critical battery. If you are connected, you can still control the aircraft quite a bit, get it out of the way, and sacrifice IT instead of people.
Finally,
Failsafe RTH -- initiated from signal loss -- is different from
Smart RTH, initiated by pressing the button. The behavior in flight and response to control inputs are not the same.
Please review the details of these features thoroughly, as it seems you have some misunderstanding. And please do not advise people to deliberately disconnect their RC from the aircraft as a means to initiate RTH. This is very risky, and to be blunt, foolish.
You should always be connected to and in control of your aircraft if possible, even when flying autonomously during RTH. You must be able to cancel RTH immediately if necessary for safety, take control and fly the aircraft.