You heard wrong. You do not get all spent renown back. You carry over any unspent renown. You also get a bonus amount of renown based on the difficulty of the last playthrough you beat and the total number of playthroughs you have completed.
The fastest way to rack up NG+ renown is repeated speedruns. On Normal + Casual, you can spend a bit of renown at the start to get Byleth's Authority and Sword skill up, equip Byleth with a strong battalion, and proceed to solo the entire game. Skipping all cutscenes, combat animations, free days, and instruction means you can complete a run in less than 5 hours, maybe as little as 2 hours. Just before the end of the game, spend all your money on cheap seeds, then sacrifice everything in your storehouse to the pagan altar.