I had a dog that was like this (she's since passed away) and one thing that really helped was teaching her a bunch of stupid tricks. First of all, I think the one-on-one focused attention involved in the training itself, even though we were only doing it for maybe 15 min per day, helped meet that need. Secondly, when she'd start going into LOOK AT ME, LOOK AT ME mode when other dogs/items/people/etc. were getting attention, I could ask her for a trick to...earn, I guess?...the attention, rather than having her nudging and pawing at me. Eventually when she wanted to steal attention she'd offer a trick rather than physically badgering me. It didn't totally cure the attention hog issue, but it did make it less intrusive and less incessant.She constantly(and I am not exaggerating the constantly) wants attention. If one of my other dogs is getting attention, she pushes her way into the mix. She will paw me (which hurts badly) if she is not getting attention.
If you're looking for good ideas for tricks, check out "Do More With Your Dog" - they have lists of tricks leveled by difficulty, and lots of youtube clips on how to teach various tricks step-by-step. The nice thing with trick training is that you can just skip or modify any that are physically difficult for you or the dog, or that just don't seem fun or feasible.
I think the problem is that your premise - "At four months old, puppies are like clay - you can mold them into anything" - is simply factually incorrect.I gave two options of what the issue could be- yet people always pick out the wrong bits instead of pick out the statement that relates to them the most shrugs