Yes - The Weather Would Be Different
Before we begin, let's go over what jumped out at me here is that you stated that your world has:
- Expanded the Atlantic ocean by 1,350 miles
- Contracted the Pacific ocean by 1,350 miles
- (by #1 and #2) Blocked all or most interactions from the Arctic and Pacific oceans
- Been in this state for 250,000,000 years
The long/short is that you have obviously disrupted the flow of arctic water in this world and have pushed continents very far in two directions - and it has been that way for a very long time. The idea that this would NOT create a change is unthinkable.
What Would Change
Here is some work about what occurred when the Bering Strait closed. It's an interesting read, but here are two key points from the article:
With the flow of relatively fresh water from the Pacific to the Atlantic choked off, the Atlantic grew more saline. The saltier and heavier water led to an intensification of the Atlantic's meridional overturning circulation, a current of rising and sinking water that, like a conveyor belt, pumps warmer water northward from the tropics.
This circulation warmed Greenland and parts of North America by about 3 degrees Fahrenheit (1.5 degrees Celsius)-enough to reverse the advance of ice sheets in those regions and reduce their height by almost 400 feet (112 meters) every thousand years. Although the Pacific cooled by an equivalent amount, it did not have vast ice sheets that could be affected by the change in climate.
It should be noted however that the article discusses this event in context of a global ice age (which caused the straight to "close"). In your world however, it has simply always been that way. So you should expect some permanent warming the the Atlantic, permanent cooling in the Pacific (due to the larger "hole" between the arctic and Pacific ocean pumping more fresh water down that way).
Another Major Caveat
That said, I actually expect that moving continents that much would have a larger impact on global climates by either allowing more area for new crosswinds to develop between continents or reducing opportunities. However there is no research available on such a fictional world, so I cannot supply a guess as to the impact while the "hard science" tag is in use.