Your rifle is a great platform to begin with. Welcome to an addiction that will drill a big hole in your wallet! It will be really fun though.
Your VX1 is a good scope. If you decide to send it to the Leupold custom shop, you might consider just changing the elevation knob. This will help keep costs to a minimum.
Alternatively, you may be better off just changing the scope all together. Bushnell makes a couple of affordable options:
Bushnell 5-15x40 Elite Tactical Rifle Scope
Bushnell 10x40 Elite Tactical Rifle Scope
The 10x is a good scope and I've had several and loved them all. My cousin has the 5-15 on one of his rifles and likes it.
As for the consistency issue, you may find that when the barrel heats up, your accuracy will begin to open up. My nephew's rifle will shoot .5moa or better all day...provided you let the barrel cool ever couple of shots. Those factory sporter barrels have a pretty light profile and heat up fairly quickly.