One of the great things about this game is you can pretty much do whatever you wish to within the allowed game mechanics.
If you think attacking other players is the right thing for you to do, you don't need to ask anyone anything, go for it!
How they respond to your attacks and how you cope with the bounties and other consequences of doing so is what could make this a truly great game. See below for "could".
It's only griefing if you continually attack the same player. I'd see it as a great opportunity for some roleplaying if you're happy to accept the consequences.
So get a bind with a short and sweet sentence explaining why your attacking them, have it on a bind so you don't need to type it each time.
Doing so will mean even if someone does keep coming back multiple times, you have legitimised why your are attacking them - because they keep coming back, despite you claiming that area of space. You could make a pretty good case to FD doing so, if you get reported for attacking the same player multiple times (so long as it is not every 5 minutes, if you see what I mean).
All of that being said, here are the POSSIBLE drawbacks for you with your plan and what you need to consider :-
1 - They just go Solo and keep on truckin'
2 - They put you on ignore and it's unlikely you see them again - even in open
3 - Anyone who has half a clue how to play will 100% escape you every time you interdict them while giving you the finger out the left window and FSDing out of there long before you do (if you even win the interdict mini game)
4 - You will soon start getting rep hits, possibly undoing the work you put in to getting Allied status in the area
5 - You start getting bounties. Unless your happy to build them up, you will have to keep paying them off. This costs you money.
6 - You bite off a bit more than you can chew and start getting killed. This costs you money.
7 - Pirating players is pretty hard to do and make money, see previous two points.
8 - You start getting reported for griefing, and even though you are not, you end up on FD's hit list and get segregated away from other players for being a mean and nasty person in this PvE game!
So as you can see, the way FD have designed the game and implemented the game, while I 100% support what you would like to do, the reality is it is unlikely to work and probably going to be quite painful for you instead.
Which is a real shame, but that is how it is in FD's Elite "Dangerous" world, and I really don't see that changing much. We all need to accept that Elite is very much a PvE game, a million miles away from something like EvE or Star Citizen as far as combat with other players is concerned. FD don't like or want Elite to get a rep for players killing each other and have very much designed it this way over time, especially given the fun that was had during Beta (sorry I meant griefing to all who complained about getting killed in the Beta).
If you want to actually do any PvP/pirating/roleplaying such as you describe, I think you'll need to wait about 5 years for Star Citizen to actually come out, or for them to actually achieve something beyond selling you more and more ships and letting you have a toddle around in a ship hanger and play a very limited and broken demo of an arena style game.
For the space games in the future they will look like this in my opinion :-
Elite - top of the line PvE & Co-op game in space
EvE - top of the line point and click space game with real nastiness and harsh consequences possible.
SC - top of the line space game that has a bit of everything, and a bit like CoD in space, bit of a middle ground between the other two.
To be clear - nothing wrong with any of the above, they are all going for a different market, which is a wise thing to do!
While I won't go back to EvE as it really can be life sucking and did feel like a second job to me after a few years, if I want peace and quiet and a bit of co-op in the future I'll play Elite, if I want to play with my guild and PvP I'll be in SC.
Whatever you decide to do, the very best of luck Sir!
