Unless I missed it you don't say what distance you were shooting at. From your post I assume it's 15 yards. For someone who's only put 1500 rounds downrange, I think you're doing great. I also think you're not giving yourself enough credit if you think you can't do any better. I've seen threads where people post their results and (if they're being honest) some people are holding 2" groups at 25 yards. That is damn good.
The advice about doing lots of dry firing is right on. You will definitely improve. Also, remember sight alignment and FOCUS ON THE FRONT SITE.
One final piece of advice, don't get too hung up on slow fire accuracy alone. Start mixing it up with some rapid fire shooting (a whole different challenge). Try moving around. Shooting around improvised barriers. (All this assumes you have access to a range where you can do this safely). Remember, in a real life situation your target isn't going to stand there for 30 seconds while you carefully align the sights and slowly squeeze the trigger.
