I've searched both online as well as this forum, and this is the only thing I can find that's similar to my issue. Albeit, not very helpful: https://www.evolutionm.net/forums/ev...vibration.html
I'm also in a '14 MR

This is my first winter with a tune, including high-flow cat and 3-port. The temps are very cold in Minnesota.
I had the TC-SST out (same shop, different time) to fix the infamous shift fork magnet issue, and I had a new valve body/mechatronics unit put in as well; also replaced the internal filter. I've seen some very slight fluid dripping, like a gasket didnt seat or seal fully between the engine and TC-SST ? It's minimal, but noticeable when I do oil changes. I doubt the TC-SST is dangerously low on fluid.
I used some old mineral oil that a tenant of mine left, 5W-30 and ran it for about 1,500 miles. The issue cropped up before I changed this oil, but it could be coincidental because the temps are getting colder.

The two main things are my engine sounds different when I start it and when it's running. I've never heard it like this, no matter how cold it's been in previous winters. A grumbly sound like the engine is struggling and not running smoothly.
The other is there's some vibration I can feel through the throttle pedal (and only there really) when I'm low-throttle between about 2 and 3k rpm's. If I'm past about 25% throttle, or in any other rpm range including idle, I dont detect any throttle-pedal vibration. Finally, if I let the car warm up fully it does seem to reduce the degree of vibration to some degree.

Any ideas as to what I can do here? I dont think it's a tire balancing, transfer case, differential, or exhaust (hole or loose muffler, etc) issue

 

Its difficult to say exactly what it is you are feeling. The only thing that comes to mind for me, is maybe youre hearing/feeling valvetrain noise from the head. The 4b11, like some engines, but unlike others, uses direct valve actuating. Basically there are no lifters or rockers being used in the head. The lobes on the camshafts act directly on the valvesprings. Each valve spring has a bucket cap or shim, to achieve proper lash. When the engine is cold, the gap between the lobes and the buckets will be larger, which causes increased noise and vibration. As the engine heats up, all the metal grows, including the lobes and buckets. That heat induced growth will actually work to reduce lash, or the distance between the lobes and the buckets. Once everything is up to operating temps, the noise and vibration from the valvetrain, should basically cease. Id imagine that when its super cold, not only is there a decent amount of lash, but id venture to guess that the rubber isolaters in the engine mounts themselves, actually get stiffer as well. Personally, i run solid front and rear motor mounts on my car. I can tell you that stiffer mounts most definitely increase the amount of vibration you feel through the pedals, steering wheel, etc. So if the cold temps are causing the rubber to stiffen, its possible that youd feel more vibration. Hopefully this helps you some. Whatever it may be, it doesnt sound like you have to worry too much. As long as you check your oil and coolant, keep an eye on temps, etc, you should be good. Youll know if something is truly wrong. Evo 10's seem to do a pretty good job at alerting you to problems, one way or another. At least thats been my experience.

 

Thanks for your reply. It's been getting better lately. I have a feeling the mucky oil leftover that I used is working itself out. I'll change the oil more frequently the next couple changes to keep it fresh. I think it is the oil, and not any other cause. I did not know what you described about the valves. It strikes me as odd, the timing of this stuff happening. I cant help but think the oil was the direct cause, but I cant be sure.
It doesnt sound as bad when I start up, and upon warming up there are minimal symptoms. I have a feeling come this spring I wont have any issues at all, which is refreshing.