ZDoom

The movement code in ZDoom has seen several changes and some of these actually do interact with the pushing stuff.

It's strange how it's different for the two versions though. I completely forgot how it worked in vanilla Heretic until someone mentioned it in Doomworld, but there is a noticable difference.

I doubt this will give you what you want. There is no slowdown when pushing, but the way this affects velocity-based movement, this can result in blocked moves which get perceived as slowdowns.

Sorry, there's nothing that could be done. This is all the result of an originally piss-poor implementation depending on several side effects and bugs in the movement code.

Recently, I noticed a difference between GZDoom and vanilla Heretic when it comes to pushing those pods around. In the original Heretic, the player was never slowed down (or maybe barely slowed) when pushing a pod around, but in GZDoom, you are. This is why I'm suggesting PushbackFactor, which would determine how much of a slowdown the player receives when you're pushing something. 0.0 means there's no slowdown at all, while 1.0 (the maximum) stops the player every time he makes contact with a pushable thing, though the thing gets pushed anyway.