Barrels on HK style weapos are always pressed in through the trunnion from the back side with the exception of the PSG1 and possibly the MSG90.  The other barrels are just not stout enough to press in the way you started.  I have a tutorial up on another site, but here are a couple of photos to make it clearer:

The barrel being used in the photos was one that someone had galled up by pressing in correctly. I bought it from him then did a tutorial on knurling it to raise the metal then then turning it back to size. Pressing it back in correctly was the next step.

The brass piece is something I made to guide the barrel in. It is very important that you get the barrel started in straight as you press.  The brass piece is smaller in diameter than the barrel. There are a couple of tricks you can use to get your barrel gap just right, but each gun will press to depth at a different height do to differences in the carrier, LP, bolt head, and rollers.  HK builds usually end up with about .015" sticking up out of the trunnion whereas Cetme's are more like .005".

It is espoused on several sites that if you go too deep you need to press the barrel all the way through and try again. That's how I ended up getting a badly galled barrel for little money. The fellow kept pressing it through until it was too loose.  Personally, I don' thave a problem with tapping it back a little bit.

Glad it worked out for you! On to the pinning, then the rest of your build.  Pay special attention to setting the gap on your cocking tube before you weld it in (and use a good heat sink .706" in diameter),  then the next tricky part is fitting the mag catch.  Post some photos when you're done!