The Way drum is a 5.5 inch shell. BDP is one of the more common of Way wraps (although all of the drums are fairly scarce). If you were going to find an Aristocrat, it would not be a surprise to find one in this size and wrap.
Stamps from George Hamilton's shop are very cool. It is surprising that the drum does not have a rectangular aluminum George Hamilton label underneath the badge (most drums from his shop do). These sometimes fall off, but there is often a ghost of the badge left (I can't tell from the photo if this is the case or not).
Way drums did not come standard with tone controls, but they sometimes have them installed. Way offered one model in his catalogs (W&A I think), but a lot of different brands were used. Hamilton could have put it in at the customer's request at some point, or it could have been installed at the factory.
The one that sold on Ebay within the last month had some condition issues, but it was a 6.5 inch drum - much rarer. It would have gone for a lot less than $350 or so if it was a 5.5 inch drum.
As far as value, in that condition with replaced parts probably between $350 and $450. I've never seen one with the Wayco strainer installed. Those strainers were used on Way Tuxedo line drums (which are rare), and on some parade snares. If George Hamilton confirmed that they would replace Aristocrat strainers with Wayco models, that's new to me. I would have guessed that someone found a parade snare, and thought the Wayco was the best option available next to having the correct Aristocrat (4th version, as that was the one with the vertical hole spacing that matches the Wayco).
If someone could find enough original Way lugs and the correct strainer, then the drum might be $500-$600 on Ebay, but you might have more money invested in it by that point.
By the way, those Wayco strainers are pretty nice, and not common. I'd be tempted to leave that one on the drum as it is part of the unique history, especially given the contemporary 1961 repair stamp inside.
