+1 What Tinker and Daryl have said....
Measure the twist and slug the bore about 2" in front of the chamber. Both my 1870's vintage Alexander Henry and Rigby .450's measure at .465" groove. The Henry is a tapered bore with Henry rifling, the Rigby is not tapered and has shallow Rigby (sorta Metford type?) rifling.

I would bet that your Purdey was regulated for a 270 grain bullet based on the 3 3/4 Dram loading.
According to Hoyem the standard hunting load was 110 grains of powder and a 270 grain bullet.

For Black Powder Loads:
Try a 300 grain paper patched or cast grease groove bullet and 110-120 grains of Swiss 1 1/2. Lighter bullets "should" get your velocities up as well while giving less muzzle rise so lower impact on the target.
You could even hollow point a 300 grain grease groove bullet to get the weight down to ~270 grains, or paper patch a 260-280 grain .45 handgun bullet up to size.
I would suggest at least a 1/8" grease cookie of SPG. Put a wax paper or bee brood foundation spacer on the powder (to keep the grease cookie from contaminating the powder), then the grease cookie, then a veg fibre or milk carton wad, then the bullet.
If you need to take up more space in the case between powder and bullet I would use grease soaked felt wads or .45 Caliber Wonder Wads.

IMO, the heavier bullets such as 325-350 grain are going to only work with Nitro for Black loadings. H4198 will be your "go to" powder choice and then case filler of Dacron, Kapok, or foam backer rod.
Of course as with all double rifles.....your mileage may vary.

- Mike