Critter: When I shot a lot, I was stacking arrows at 20 yds with my Browning recurve, no sights. Anyone can do this. Once you get your bow and arrows tuned, it's just a matter of focusing on the smallest spot possible.. a meditation. Don't be lookin' at your arrow, or anything else,, just what you want to hit.
It's probably not your bow. Please look for articles on "tuning" your bow and your arrows. The addition of anything to your bow, or your arrows, will change the way it shoots, usually, by slowing your bow down, requiring softer arrows; or, if the mass is added to the arrow, it will soften the arrow and you'd need a stiffer arrow. Both can/will have dramatic effects.
1st: There's a magic spot for your nock point; check to see what your bow maker recommends and what other bow makers recommend, to get a general range. Get yourself a bow square and a tool to attach and remove a nock point. After I find the sweet spot, I tie a nock point with dental floss and get rid of the metal. Your broadheads may require a slightly different nock point than your field points, depending on the weight and dynamics.
2nd: Sounds like you've changed the bow and therefore the arrow spine required. You can best play with this by getting a wide range of field points, from 85gr to 145gr; and you can add weight to them. 25 grains of tip weight equates to 3 pounds of draw wt.
3rd: Another major effect of your arrow is length; 1"= 5 pounds of draw wt!!
Since you've added something to your bow, I would imagine that you've slowed it down, requiring softer shafts; just for grins, try adding 25 grains of tip wt., or shooting a longer arrow and see what happens. If it's going the wrong way, change up and reduce tip wt. shorten your arrow.
There are a lot of things that will affect your bow's performance, including what type/mass of string you have and if you use silencers what the mass of those silencers are and how far from the bow tip they're placed.
Changing your brace height makes a difference. Find the recommended range for your bow. Even a couple twists of the string, one way or the other will affect your groups.
Your arrows should wobble a bit, coming off your shelf, but not radically. Again, find some info on bow/arrow tuning and don't sell your bow yet. Bows are like musical instruments; one tiny thing can be slightly off and it can produce drastically bad results. But when it's right, the music is sweet!
Good luck!!..... Ken