Pilot reported engine roughness during departure. The pilot decided to troubleshot and continue to the original destination. The issue got progressively worse; but the pilot was able to safely land at destination.

Narrative

Having flown to ZZZ for lunch; I left ZZZ with a destination of ZZZ1 (home base). Shortly after climbout I experienced rough running [engine]. The engine was still producing power; but it was obvious somethings was wrong. I was able to continue climbing as I tried to diagnose issue. I checked fuel pressure (OK); checked oil pressure & temperature (OK); isolated individual magnetos (same roughness on each); adjusted mixture settings (I could make it worse but not much better). I looked at EGTs & CHTs and noticed cylinder #4 was abnormally cooler than the other 5. I deduced I had a partial combustion issue with number 4. Since the Laser has a glide ratio similar to a brick; I decided best course of action was to stay as high as possible until over the airport. ZZZ1 sits below the upper tier of ZZZ2 class C; so I called ZZZ2 approach and requested a high orbit over ZZZ1. As I approached ZZZ1 the engine cleared noticeably. As I arrived over ZZZ1 I contacted ZZZ1 Tower. They gave me priority landing and I landed without incident. Tower at ZZZ1 was also very helpful. Upon taxi to hangar; a runup to max brake holding power was done with little to no roughness noticed.After the engine cooled; I pulled spark plugs & inspected with very little variation between cylinders (not unexpected as the problem cleared at end of flight).All 6 injectors were carefully pulled & inspected. All clean except a speck in #6!Fuel flow from fuel divider into 6 graduated cups showed no anomalous variations.All 6 injectors cleaned & reinstalled.Spark plugs reinstalled.CHT/EGT temp sender wiring was verified.Fuel sumped.Engine test run on ground with no issues.Engine data downloaded for review at home.Engine re-cowled.After review of engine data; CHT/EGT plots for #6 showed some minor anomalies; but not as bad as #4. Today (DATE) after another ground run; a test flight was performed. Engine ran smoothly and developed normal power. Assumption - Partially clogged #4 injector that then passed the debris and minor clog in #6 injector that was removed when cleaned. Both ZZZ2 approach & ZZZ1 tower were very professional and accommodating.