Jason,
According to Dr. DeWitt Bailey, the pre-eminent scholar on the Brown Bess, no "King's Pattern Musket" or British Board of Ordnance (Government) issued Brown Bess with the flat bottomed P1755 lock (as is on your Pedersoli Bess) ever made it here in the Colonies during the FIW. SOME P1756 and P1760 Carbines with that flat bottom P1755 lock made it here, but those had smaller "Carbine size" Locks and .66 Caliber barrels, so that conversion would be out of the question.
THE most common Musket used here in the FIW was the P1742 Musket with the banana shaped lock that Dave Person mentioned and the wood ram rod. The standard barrel length was also 46" compared to the "Short Land Pattern Type" 42" barrel on the Pedersoli Bess.
Now some of the P1742 Muskets were shortened to 42" barrel lengths here during the war and bushings put in the larger diameter wood ram rod pipes to use a Steel Rammer as well as a retaining spring in the entry pipe. They also added either sheet metal brass nose bands to the stock near the muzzle and even some had cast brass nose caps fitted to them, as on the Pedersoli Bess. HOWEVER, the banana shaped locks on the P1742 rules that out as a conversion on your Pedersoli Bess.
Please understand that virtually every FIW reenactment group allows the Pedersoli Bess to be used for FIW reenacting, even though it is too late for the FIW War. This because for a very long time the Pedersoli and the Miroku Jap Bess (also a copy of the Short Land Pattern Musket) were the only readily available/affordable Muskets to do FIW period.
Now after possibly dashing your hopes, I do want to mention that British COMMERCIAL Muskets (Not Made to British Board of Ordnance/Government Patterns) WERE used here during the FIW with wood ram rods and the flat bottomed P1755 Lock (as on your Pedersoli Brown Bess). Barrels were also 42 inch length and they used cast brass nose caps as on your Pedersoli Bess.
One of these Commercial Muskets is on display at the Valley Forge Visitors' Center Museum and another is shown and the photo can be enlarged by clicking on it to see it better, in the following link.
http://www.adirondackbasecamp.com/2013/04/rare-french-indian/
To change your Pedersoli Bess to this configuration, you would need to do the work and add the larger wood ram rod pipes that Dave Person mentioned above. Technically, you would also need to fill in the engraving on the lock plate and have just "Wilson" or another known Commercial Musket Maker's name engraved and also thin down the trigger guard a bit. However, that kind of lock plate engraving modification is usually beyond the abilities of most amateur hobbyists. So normally you would need to have it done for you by someone else.
Gus