No, don't push forward!
I haven't done them in R22s, but have practiced numerous engine-offs all the way up the transition slope in Squirrels, and they can be done easily.
Of course, if it happened without forewarning when fully loaded it might be a different story!
The basic principles are easily seen if you consider the opposite 'ends' of your transition from hover to steady climb:
Taxiing auto - freeze collective, keep tracking the way you're heading, settle, cushion.
Steady climb - Lower collective smartly and fully, adopt auto attitude and IAS, wait, flare, level, cushion.
In between, there's obviously a sliding scale of things you do, 'morphing', if you like, between the two extremes.
At 20 kts and 20 ft, say, you'd be able to get the lever down a bit and flare a bit, giving it away when the tail's nearing the ground to run on (or hook in really hard to get zero speed if the ground's not favourable).
At 40 kts, 50 ft (for example), you're probably going to be able to get the lever fully down and get a decent flare in too.