You should complete your Oil change interval as usual e.g if you change oil @ 3000 km then do it after completion of cycle.
Let me tell you that I have used following Oils in my Cuore and honestly all of these oils felt the same as far as smoothness and petrol consumption is concerned.
The difference lies in Engine sound, smoke feedback smell and texture etc. Its a top down list where the oil on top is the best in my opinion;
LM Super leichtlauf 10w40 (least smoke smell on start ups and on high rpm thrusts. Lowest engine sound of all. OCI@6000Km)
Castrol Magnatec 10w40 (very similar to LM in all aspects OCI@4000Km)
Shell Helix Ultra 5w40 (Smelly fumes, fastest burning oil of all due to seepage past my weak seals, color of oil changed within 3-4 days to quite dark brown. I suspect it isn't the cleaning thing as this oil is supposed to clean engine top notch. My engine is already clean from inside due to past usage of synthetic formula oils. The quality of Helix Ultra I doubt is not same as International and I believe it suffers oxidation. OCI@6000km nearly black color of oil when thrown out)
Shell Helix HX7 (same as Helix Ultra, additionally noisy due to thinner oil weight (5w) at startups only not after warm up. OCI@5000km, black color when thrown out)
Toyota Mineral 20w50 (quieter engine, sluggish/heavy feel on accleration, engine flushed at the end of its usage and moving to synthetic formulas and found bit of gunk coming out. This oil Changes its feel after 3000 Km unlike above mentioned oils as they do not change feel of smoothness at all)
+I only use either Toyota Denso Thai made Oil Filter or Nippon Micro Japanese filter. Nothing else.
Rings are changed when there is excessive blowback in crank case. Excessive oil seepage past rings and seals. Excessive oil reduction e.g if your oil is reducing at the rate Greater than 500ml @ 1000 Km. When the head is Opened it is wise to change all at once namely; Head gasket, Rings, Valve seals (signs of weak engine) and even the clutch plate, pressure plates and bearings if they are needy too as greater modification and opening of engine is required to change so these should be done in one go to save time and cost. Oil reduction issue when becomes worst you will see it in city driving too.
I have EFI in my mind but cost is over weighing the benefits in this case. My engine and components are in good shape and I am consistently getting 18 km/L on the minimum side and 21 Km/L on very long trips such as visit to ISB and back. In city I am getting 14-15 Km/L. I would think of eFI with full engine swap some day after my Rings/Pistons/Clutch plates all require work together.
Also in previous posts I have seen your comments about Black smoke. It is much because of rich mixture settings (more fuel and less air) instead of bad rings/pistons. Please get your carb adjusted for mixture settings from an expert mechanic. If the smoke is puffing clouds of dark grey/bluish smoke when you dip the gas pedal then it is rings/piston thing.