Most Mk 1s do not have the correct parts and, since you don't have a Pedersen Device, work just fine with standard parts.

How is the muzzle? Any dents or burrs that intrude into the rifling? If so, recrowning may restore accuracy. On the other hand, if the last 1.5" of the bore is worn, not much can be done for the barrel. As others have noted, handloads may help. If the 150 gr GI bullets at reduced velocity don't work, try some 180 gr or 200 gr round nose, flat base (commercial soft point) bullets. They have a longer bearing surface & may stabilize. Try groups at 25 yds to see if the bullets are keyholing - sounds like yours were keyholing (tumbling). They should hit the paper at that range. Avoid any boat tail bullets - boat tails are near impossible to stabilize in a worn bore.

One other thing to do is to make sure your guard screws are tight. From the degree of inaccuracy you describe, I doubt this is a factor but it's worth a try.