You could bind it to a hotkey. Open the console, type [bind p "turbo 255"] (quotation marks included, brackets not) to, for example, make the P key speed up your movement. Like any keybind, it will persist through quitting/reopening GZDoom, and all you'll have to do when starting a new game is hit the key.
@Actraiser, try disabling weapon bob, too. I forget where that option is, but if you find that, see what it does for you. ^_^