All of the following is intended to be taken within the context of "in my opinion":
Yes, ST 7 is too high, and you already know where to go with those 2 points - into PE. Higher gun skill compensates for Hit Chance penalty from low ST, so just go with higher BG. 180 is minimum to get BRoA but don't stop with 180. Get 200 and MRD is an option. Get 240 and you can hit at longer distances. Get BG 250 or more and you do the least deterioration to your weapons.
Next is IN. 6 is too high too, but really it depends on your target level. If you absolutely must be done earlier, then 6 might be just right. But if you're more casual about it, are not in a rush, and willing to level more, then make IN only 4 and put 2 more points into PE (or LK).
Drugs? Yes. Even for PvE. You get into the habit (no pun intended) of drug use which later translates well to PvP playstyles. Wondering about a ST-related Hit Chance penalty? Buffout is your buddy. Do Nuka-Cola with Buffout. Want to act tanky? Then Psycho is your big brother, which is one reason you need higher PE. Want the final toughness advantage? Beer is like your rough-housing cousin, and yet another reason to pump up your PE. Get some PE back with cigs.
Which leads me to Luck 1. I don't like it. You could go IN 1 and avoid the lowest Luck. Or ditch all your PE, become an up-close tanky fighter, and have high LK. Low PE means you drop into encounters much closer to targets, so the fight begins more quickly, thus you get that XP sooner and you're onto the next encounter.
Good tags. Fast Shot, fine. And consider Good Natured. You can recruit a human companion follower that way, level him up, and bring him along to help find locker loot. He will also serve as a mule to carry stuff when you're overweight. Get Speech up to only 125 later, at your leisure, and get a 2nd follower. Now you have 3 guns shooting at enemies at the same time.