Good on you for focusing on the irons. A better target would help a lot. In my experience that type of target combined with my vision doesn’t allow me a consistent point of aim. Depending on the range, I really like the various NRA bullseye targets. It’s probably not a coincidence that they match the width of a standard front sight post… 
How accurate can iron sights be? Well, the smallest groups I’ve ever shot in my life with the exception of highly magnified bolt actions were with iron sights. Again that has more to do with the way they line up on targets than any inherent accuracy advantages, but you can do better than you were doing.
A good goal is 4MOA with good ammunition. At 50 yards that means 2". Some folks can do better(and it should be your goal,) some very competent people will do worse for various reasons, but in my opinion that’s the zone where competence lies for most folks.
So tips…in no particular order.
1)Leave the front sight in the rifle. It’s the size it is for a reason.
2)Learn about natural point of aim, and then apply it to every shot.
3)Get prone if your range allows it, unless you’re heavily sandbagged on the bench in my experience prone is better and more consistent.
4)Learn about follow through, and apply it to ever shot. At your level, and when zeroing this means the rifle should have completed it’s recoil and have settled down before you allow the trigger to reset forward.
5)Remember to breathe between shots, and don’t get caught up in stopping halfway through…breathe in, breathe out, fire the shot.
6)Don’t try and make the gun fire NOW. Learn to build a good firing position and once you’re there, and the natural point of aim is good, focus hard on the front sight and roll the trigger back.
7)Dry fire all of these things over and over.
8)Get professional instruction…I’d also highly recommend getting a subscription to panteaoproductions.com, if only for a month. Tons of videos, from men at the tip top of the field who aren’t teaching anything that isn’t proven. Paul Howe’s videos on there are full of fundamental gold.
ETA:It wasn’t bad shooting, so just take my tips as things to think about as you progress.