Recrowning is first priority
The trouble with muzzle wear is that it is usually assymetrical at the crown. This can be a sort of statistical chance thing at first, but any unevenness, such as a nick, tends to lead to a vicious circle: Where the bullet base first parts company with the barrel, there will be a puff of very hot, very fast gas coming through the gap before the base has completely left the muzzle. That tiny puff on one side pushes the bullet off the barrel center line, giving it a skew. The mechanism is similar to throat erosion - if not so severe - the spot tends to be eroded and the unevenness will be worsened. Maybe be only microns. But work out how much skew over the length of a bullet will give a bullet 1 MOA yaw, and the result is awfully small.
If all this did was to divert bullets off course by a couple of MOA in a consistent direction, the deviation could be corrected by the sights and there would be little trouble. Unfortunately, since the bullet is rotating, it is not a simple straight-line deviation, and tiny differences in velocity will vary the effect of the "kick" produced by the nick or wear on the crown, and thus the magnitude (and direction) of the deviation from the barrel center line. In other words, the group opens up all over.
Nicks and uneven wear caused by careless cleaning are the major causes, and the worst offender is a dirty pull-through cord or a chain (as favored in Germany). Careless cleaning can, in fact, be over-enthusiatic cleaning. No-one can pull anything through a barrel dead straight down the barrel center line over a distance of a yard without touching the sides, which is why the Swedes and the Swiss had little sleeves to fit over a cleaning rod and protect the muzzle. Without this precaution, some poor grunt cleaning the heart out of the barrel to please sarge is probably doing more damage to the muzzle than a sackful of ammo. Bad experience has taught me that the shiniest barrels can be the worst.
So what is to be done? Just recrown the barrel. It is explained in detail, with good photos, in the very first chapter of "Accurizing the Factory Rifle".
If you have a delicate touch, you can probably get a crown cutter and do it yourself. If not, go to a good gunsmith (i.e. one who doesn't just want to sell you a rebarrelling job) and it will be the best 10-15 dollars, euros or whatever that you ever spent on your rifle.
In the case of the rifle that is the subject of this thread, I would do this before spending more on ammo. You may well find that the dispersion of the shots shown in the targets is much improved. Of course the ammo and the shooter also play a role...;)