Oh! I see!
I use gamemaker studio but I can understand this pretty well, the only problem about my situation is that I have to make my own physics and movement and collisions and stuff without built in physics.
The problem is that I can easily divide my speed in half or something, but multiplying for example 2 to a below 1 decimal causes it to get kinda' weird, it's hard to explain.
The way I set up friction (if only barely) is by multiplying my horizontal speed by a decimal (in my case it's 0.9) which causes it to slow down. But when multiplying this by 2 or something, it's above 1, which just accelerates the character instead of slowing it down.
I could just make it so that there's a cap to the friction, but I feel as though it will - if only slightly - change the game mechanics and could be abused, I could of course just make it so that you can only slow the game, it would mean you couldn't speed up the game but that's not really the point of the game-speed mechanic.
But still I like the way you do it as well, first you set a minimum speed of sorts, and then your able to just change it on the fly, I think that would work pretty well if that pesky DIY physics weren't in the way (for me at least)
Also, thank you for helping!