Well I think there are three Emperors which are your best bets:
1) Otto III - that wouldnt be a HRE as we know it, though, not German and led from Rome
2) Frederick Barbarossa - Barbarossa might have managed on the strength of his arms alone, but of course the problem remains that those arms always had to cross the Alps - when he was in Italy, the German nobles rebelled and when he was in Germany, the North Italian cities rebelled.
3) Henry IV - Barbarossas son, and his "Erbreichsplan" to make the Imperial Crown hereditary, which very nearly passed. If it does, then there wont be so many dynastic conflicts in the HRE, potentially allowing it to centralise.
After Henry IV its too late - his son Frederick II was practcially only interested in Sicily and gave away vast amounts of rights to th enobles (some of which de facto they already had enjoyed before, but still, codifying them meant a huge loss of imperial power), and after Frederick II came the devasting interregnum...