Steve,
Don't know your level of WW expertise is, and I haven't seen what your using for a plane. So don't take this as gospel or if the problem is more complex, as an
insult to your skills. Still with what you have described, the symptoms sounds like the problem might not be the plane your using, but how it is set up.

It sounds like the blade setting (angle and depth) and how its sharpened might be the problem. If your on soft wood like cedar any plane that's got a good edge and setting should pull up the right thin shaving off the top. It also might be you have it set too deep.

A plane that is digging in, then not digging in at all, and sometimes ripping out grain sounds you have a dull blade that is also set to deep. A blade set to deep on to sharp an angle will dig a wedge that gets stuck in the shaving slot and as you continue down the board will pull out. As the slot plugs it will stop biting at all.

I guess, I'd suggest before you buy a new plane, try honing the knife edge to sharp at the recommended angle, using a good stone. Don't forget to pull off the blade over. Sharpening pulls metel over the edge making a sharp edge thin but rounded. Then when you put it all back together, pull the blade back, so the cut is not as deep. Your looking for thin shavings. Also raise the shim. This will dropping the angle of attack (up and down) on the blade.
Then angle the blade a little left to right a bit so you have a leading edge on the steel.

After you have reworked those three issues, test the setting on some softwood. If its doing the job evenly producing the thin curlyques you have it right, then move it up to hardwoods if they are part of your project.

If your looking for a new plane for working strips look at finger planes. They are about 2 inches long by half an inch wide. Its not that they are better at doing the job of shaving something down. Its just that being smaller they are easier to work on smaller edges ....like strips. Its more of a control thing rather then how a blade works thing. The down side is finger planes don't give you the length of soul the make for a really even run across a board. So its a trade off thing.

Let me know if it makes a difference

RUSS