It's not a replica anymore, it is a Hero's sword, just not THE Hero's sword.
He went from wanting to recover a work he was ashamed of to being proud to have made the hero's "partner", the sword that felled the demon lord.
The original Great Hero in this story was the elven warrior Kraft (now a priest) and we can see in Ch. 34 that the legendary Hero's Sword was HIS sword. It is very likely that the Village of Swords "prophecy" about the hero coming to pick up the real Hero's Sword was a garbled transmission of Kraft, after retiring, leaving his sword there and telling them that one day if he's needed again he would come back to pick up the sword. We already have a similar story with the elf who hid the legendary booze. Basically the elves leave crazy legends in their wake then promptly forget or cease to care about them. The real reason no one - including Himmel - have been able to pick up the sword is simply because they're not Kraft.
So, yeah, Himmel has always been the true hero and he'd never needed Kraft's original sword. The replica did quite well as the true hero's sword and it ended up being buried in the hands of its hero.
I think the journey to the past really happened. In the first chapter, the party was content letting Frieren leave despite their attachment to her. I think that's because they'd spent this part of the adventure knowing the future Frieren would remember them and would be changed by their adventure together. They'd said their proper goodbyes.