As described not a broken valve spring as with that symptom it smoothes out above 3000 RPM.
You may have something that could be worse, even disastrous to your engine, which is an intake gasket leak. Water getting into the intake will cause stuttering and missing. Water is directed into the intake area by a cracked plastic cowl.
Possibilities from worst case:
1) This water issue is well known and can cause total engine failure if parked in the rain with the engine off. Water drains into the rear cylinders and when it is started, it hydro locks and destroys the engine.
Replace the intake gaskets now, new cowl is probably a good idea also.
2) Broken valve springs, can just be mild issue, or fatal to engine. Replace them all now. Cheap insurance, new design is more reliable.
3) Fuel pump, filter, gauge asembly, worst case can leave you stranded but not fatal to engine. Test pressure at rail.
4) Spark plugs, when were they last replaced? Use only stock replacement Champions. Others are a waste of $.
My 2004 has had gaskets and valve springs replaced after failure. Fuel pump is next.
170,000 miles and going strong.
Not trying to scare you, but why replace the entire engine if not necessary?
A smoke test will show up the gasket failure, but it is almost 100% sure to happen! along with valve springs sooner or later.