Hey Luke,
Interestingly it never shoots vertical, horizontal, or evenly dispersed circular groups. They are almost always strung at an angle from left to right or right to left.
That would indicate a bedding problem on the stock receiver fit to me. The side to side fit of the stock to the receiver can be easily bedded. Mainly the bedding/shimming is done on the 2 flat sides on the front part of the receiver to eliminate the side to side play of the receiver/stock fit. The fit of the trigger group does a pretty good job of holding the rear of the receiver in place. You can shim the receiver to test the results before going the distance of using bedding compound. The fit MUST be tight. Take out the forearm/oprod liner and put the receiver back in, no trigger group, then check for side to side play if there is any movement it needs bedding the fit should be TIGHT. Actually just check to see if there is any play at all in any direction with the trigger group and forearm liner out, that will let you know just what kind of stock/receiver fit you are dealing with. If there is side to side play then most likely when you install the forearm liner and trigger group there will be unequal pressure on the gas block receiver fit. If it is tight then re-install the trigger group with the liner out then check the fit of the gas block to the stock. It should not be bearing unevenly, or lopsided on one side or have a uneven gap with the liner out. If it does then when the liner is back in it will be putting uneven pressure on the barrel. If it is tight on one side or not a even gap then it would be best to even out the gap before bedding or shimming, if you determine you need to bed it or shim it because there is not a tight fit at the front of the receiver. Any uneven pressures on the barrel is no good, just like any rifle.
While the 223 is not a high recoil round the 1 lb+ op rod bolt slamming back and forth WILL move the receiver around if not tightly bedded. You can buy brass shimming material at a local hardware store for pretty cheap or possibly use aluminum from a soda can to test but be aware that the soft metals will deform in time because well, they are soft metals. But it will let you know if you are on the right track. I picked up a "variety" pack of brass shims in different thickness's for like $6 at my local ace hardware a few years back.
The stocks are a mass produced item, not a precision made stock. It is possible your stock is not straight either, that will be apparent when you re-assemble the rifle without the liner, I had to return a mini stock to Choate because it was not straight in the forearm and put pressure on one side of the gas block
Not being able to see the groups the question I would ask is, if you were able to eliminate the horizontal stringing would you be satisfied with the groupings? If yes then I would take a really hard look at the receiver to stock fit and any uneven pressures on the stock/gas block fit.
Here is a link to GunDocs website that has a video of how he beds the mini action, if a pic is worth 1000K words then the video speaks volumes.
http://www.greatwestgunsmithing.com/minibedding09%20low%20%282%29.html
hit the play arrow even though it says it's loading and the vid will play. Vids do take a while to load completely.
General link to mini 14 work done by GunDoc. Video selection is scroll down and to the left invaluable videos if you haven't seen them.
http://www.greatwestgunsmithing.com/mini14.htm
the shimming can be done where he beds the receiver to give you an idea if you are on the right track, just make sure you shim it with the liner out first until it is tight and the gas block gap is even (mark your shims right and left) then re-assemble with the liner in place. No vertical spread shows you something and the side to side spread also indicates something.
Also be aware that the Target Mini has a different chamber than the other mini models. It is specifically chambered for .223 and does not have the looser chamber like the other mini models that will shoot either .223 or 5.56 ammo.
If you decide to keep the mini I recommend a Choate hand guard to replace the factory one, it has way better venting of spent gases and helps keep the hot part of the barrel cooler.
Best o' Luck
WB