I'm going to go out on a limb and say that you aren't including the False Easting and False Northing in your XY coordinates. EPSG:4456 states the FE and FN values should be 2000000 and 100000 respectively. Being short 2 million feet on the easting value would explain why your point is in Pennsylvania.
If you change your point to include these values (x=2982394 y=299298) then that looks like the location you might be expecting.
EDIT -- I just checked earthpoint.us and WGS84 is the datum they are basing the calculation on. There is no State Plane Zone based on WGS84, so they're probably using the NAD83 parameters. For NAD83 NY/Long Island, the False Easting/Northing values are 984250/0 respectively. Try changing your output EPSG code to 2263 and see if that fixes the issue.
SIDE NOTE! If you are 100% positive that your data is in NAD27, then it's possible the wrong FE/FN values have been applied to your data.
Without knowing the projection, or datum of the monuments, the only way to transform them correctly would be through a great deal of trial, and error.
Given the latitude of the area you are in, the Northing is too small to be in UTM meters, or feet, unless the first digit of the coordinate has been removed for space saving.
Knowing where the monuments are on the earth, download imagery for that area.
At least you will know the datum, and projection of the imagery.
Manually plot the locations of the monuments over the imagery using the same datum, and projection as the imagery.
Now comes the fun part.
Transform the monument data from its current projection, to its desired projection, see if you are in the ball park. If not, try again with another target datum and projection.
It may also be necessary to transform from say a Cylindrical Mercator projection (Virtual Earth, etc) to NAD83, then from NAD83 to something else, say NAD27 using NADCON transforms, otherwise it is possible that the transformation is using Molodenski, or Snyder formula, and you could have significant differences.
Another solution would be to use Corpscon 6.
Then work backwards, taking the approximate values of what the points should be in CT State Plane Feet, knowing the datum, and projection, transform them to NAD83 Meters, Feet, UTM, and so on seeing if you find something that is within reason. Look past the first digit to see if the rest of the coordinate values are close. (Surveyors have been known to localize, or drop digits to save time, and reduce keypunch errors when doing calculations.)
I wish you all the best with this. This type of detective work can be incredibly frustrating.
Best Answer
You'll need to reproject them to handle this conversion.
Proj.4 is a very standard library, used by a lot of software for reprojections.
One means of using this would be to use a utility like gdaltransform to do the transformation for you.