You are correct in your assumption about shortening the barrel and re-shaping the stock into a pistol grip. It does turn your H&R into an NFA weapon. A couple of details for you:

Cutting the barrel down shorter then 18" and adding a pistol grip does not make that an AOW since it had a stock on it in the first place. It becomes in the eyes of BATFE an SBS. If you started with a virgin receiver that never had a stock on it then it would be an AOW. The tax stamp is the same cost ($200) for an AOW or SBS that "you" make. If an 07/SOT took a virgin receiver and made it into an AOW, then he could "transfer" it to you on a $5 tax stamp.