Hi Andrew
Well you have asked the million dollar question!
I would suggest that you yourself have a look at the Griffiths Valuation for the Draperstown (Ballinascreen) area - but remember that the tenants of Draperstown were not all tenants of the Drapers. So you would really need to find out more about the various landowners there. For example the Corick Bradley - the landowner was a Rev. Alex. Miller. Perhaps there were a lot of smaller landholders on that side of the mountain?
The Kirley Bradley's would have been tenants of the Drapers Co. If you try this link hopefully it will give you some background on the company. It also tells you all of the townlands that the Drapers Company had holdings in. (Hope I have copied the link properly!)
http://www.proni.gov.uk/introduction__drapers__d3632.pdfAll info about the Drapers Co. is also at PRONI.
Once you have ascertained which townland you can find and have a look at the actual lease that your "Bradley" would have signed.
But I think the key really is knowing exactly which Bradley before you can go any further - you have seen how many there are and the same names are being perpetuated within the same generation. Dad - Pat, Uncle Pat, son Pat , cousin Pat .....you get the idea!
This is where I have ground to a halt because really I need to get to PRONI and start to look though the films of the Parish registers. I hate to say it but you probably do to. If you know some of the family members you should be able start to pick them up in the registers. You almost need to draw up a couple of family trees to see who fits where to rule families out. That's the approach I coming from. But I'm sure you may be advised differently by others more experienced than I!
As you probably know PRONI will be closed as of Sept (for 9 months I think) getting ready for the move to their new premises. I think some small portion of information will be available to view elsewhere? I'm sure Aghadowey will know...
It tricky because if you're like me you probably live nowhere near Belfast. Just tread carefully because it would be awful to pick up the wrong Francis & John.
Best Wishes
Leslie