A "fast crawl" which you should only be able to use with your weapon slung on your back would help, but sincerely doubt it'll have as great an effect as you think. If you're on the floor with your weapon in your hands and a nade lands in the same room as you, you'll either have to spill it, or sling it on your back to be able to do this "fast crawl" in the first place.
Yep. I agree, that you should not be able to escape nades with "fast crawl". It is not a frog leap or anything like that.
But I think this type of movement should be aplied to game.
This kind of "fast crawl"- is very useful kind of way to advance under fire. And you actually do not have to slung your gun to do it.
When I was in service, we practised a lot of this kind of "traveling". A lot.
There are two ways to do it. Both work well with rifles and SMG:s, with MG:s it`s bit harder. Either you use only three limbs, you keep your gun in your other hand. Not so fast and effective way to move.
Second way you just keep your gun in your hand, it touches ground every time with you hand. Gun will not brake, if you don`t wish to brake it. And since there is no modelling to gun jams=>sand in machinery, or twisted sights in game, this "touching ground"-thing is not conser of any kind for realism.
It can`t be too hard to model, though there are more important things to look at first.
And it would add more gameplay- features and realism to game.