[JayJay]

Dave R: You should be able to tell if the coil has a resistor in it by checking the primary side with an ohm meter. I'm not sure what the values are, but I would think that the coil with the resistor would read something between 4-7 ohms; where you would have next to nothing on a coil without an internal resistor. I've got a 149 with its original coil installed, I'll check the value with an ohm meter and post the results.

I'm concerned, though, that the coil may not be your issue. The fact that it runs better at an RPM where less fuel volume is required makes me suspicious (although a marginal coil could present the same symptoms.)

Have you made sure that the carb is getting fuel under all operating conditions? Do you have a filter installed in-line from the tank, if so, could it be partially blocked? Is the filter designed for gravity fed, not pump fed, systems?

How clean is the inside of your tank, have you cleaned it with muriatic acid?

If you remove the fuel line at the carb, you should see a clear stream of gas.

Finally, are you confident in your carb's float level adjustment? General rule-of-thumb is to adjust the float so that it is level with the top of the carb when you hold the top of the carb upside-down. On the 149, you also need to adjust the stop so that the float doesn't bottom out on the bowl and hang up the inlet valve (Been There, Done That). If your float is missing the stop, as mine was, order a new one, replacement has been redesigned and is much more rugged.

I do think your problem is either spark or fuel related, and attention to detail will likely resolve the problem.

Edit: By-the-way, your engine should be a 321 14 HP; the 341 is a 16 HP found in the relatively rare Model 169.
(I think the Kohler numbering scheme is based on the bore diameter in millimeters, not HP.)