Hmm. The perils of buying mail order. Cumberland sells a ton of motors, but the only ones they actually touch are the ones that they sell from the actual brick-and-mortar store, such as the Remote models, which must be dealer-installed. Frankly, they probably never saw the contents of the box... it could have been filled with concrete blocks, and they would never have known. It's highly unlikely that they did a PDI on your motor. They can and must do service, but they may not want to get involved in this case -- because of freight costs. It's always reasonable to call them and ask their recommendations. They owe it to you to see that you are satisfied.
The MFS4/5/6 is a very solid design -- almost indestructible. I never understood the popularity of the 5, since the 4, 5, and 6 are identical in every respect except for the carburetor and the stickers. They are all test run in Japan (but not for very long), and then the oil is drained for shipping overseas. I suppose it's possible that someone boxed it up without draining the crankcase, but I've never seen that, and I would have expected that the oil would have leaked all over during shipping... and that would be obvious.
If the carb was primed last fall, but not run, it is very likely that crud is in the carb. That, and the fact that it will only run with choke points to either a defective carburetor (extremely rare), or varnishing (or other junk) in the passages. The warranty is there to cover any manufacturing defects. The Factory can't control the consumer's actions or abuses, so varnishing is normally not covered by warranty. Any time the carb sits for a week or two with the dirty US fuels we get these days, varnishing is expected. That is why it's good practice to run the carb out at the end of each and every day... or, if that isn't possible, to drain the carb before storing for more than a couple of days. It's OK to lay the motor down (on the correct side) for transportation, so there is no need to drain the crankcase just to take the motor off the boat.
If your motor shuts off when throttled back, the idle is set too slow, or there is some other problem. They are all supposed to idle. On page 13 of your owners manual, you will see that the motor is supposed to idle at 1100 RPM in gear, 1300 in neutral.
I show 6 dealers within 50 miles of your ZIP code. You can find them by using the Dealer Locator feature of the Tohatsu website. You may want to call them and see what they can offer you for service, especially since it seems that the dealer you went to for the PDI wasn't very thorough. That said, I would at least contact that dealer and ask about the overfilling, wrong plug gap, etc.
Overfilling the 4/5/6 crankcase will cause running problems (including not starting, not idling, and limiting power), due to extreme crankcase pressures, but it typically does not cause permanent damage if only run briefly. Once you have the carburetion problem fixed, I would expect the motor to run very well.
Please post the resolution to the problem, so we can all know how it works out for you.