First and foremost before we progress on this :) we have found a way to use high resolution textures. While some may not agree that this is an ethical process 
it can and has saved me tons of time. I'm pretty sure the limit is 4096x4096.
I'd be more than glad to split up the image for you and there are multiple GIMP methods to achieve this.
To save time for you, you can try this method.
Open your file go to new, and assuming your texture is 2304x2304 already, GIMP will offer this size. Click ok.
Go to filters > render > pattern > checkerboard and where it says size hit 256 and the box beside it you need to click on px.
Go to new and create a 257x257 (yes I got the dimensions right 
)
Ok now go to your original file. Copy it, then go back to the checkerboard. Use the wand tool, click the top left checkerboard box and go to edit> 'paste into' now you should have a piece mapped to 257x257 so right click and copy it. Go into your 257x257 file, go to new and create a new 257x257. Now, in your new 257x257 paste the 'piece' into it. Then go to image > scale image and knock it down by 1 pixel to have 256x256.
Now save it!
Go back to your checkerboard. Click ctrl+z until your pasted image isnt there anymore. Now, go to your palette and find a red colour. Fill the squares that youve done so your first is the top left. Now fuzzy select the next square, either on the right or directly below, and copy your 2304x2304 image and paste it into it.
Repeat the process shown above in bold, and when youve finished with that square, make it blue. This way you know which parts of the image you have segmented.
For some reason the checkerboard wont create 256x256 for the dimension of 2304x2304.
Obviously you want to do a block of 3x3 in the checkerboard first, and name them something like eye3x3TopLEFT01 eye3x3TopMID01 etc up to 9 different files for each 3x3, to distinguish your files as there will be a 81 files. It will be very easy to lose track if you dont do it this way.
Let me know how you do.
it can and has saved me tons of time. I'm pretty sure the limit is 4096x4096.I'd be more than glad to split up the image for you and there are multiple GIMP methods to achieve this.
To save time for you, you can try this method.
Open your file go to new, and assuming your texture is 2304x2304 already, GIMP will offer this size. Click ok.
Go to filters > render > pattern > checkerboard and where it says size hit 256 and the box beside it you need to click on px.
Go to new and create a 257x257 (yes I got the dimensions right
) Ok now go to your original file. Copy it, then go back to the checkerboard. Use the wand tool, click the top left checkerboard box and go to edit> 'paste into' now you should have a piece mapped to 257x257 so right click and copy it. Go into your 257x257 file, go to new and create a new 257x257. Now, in your new 257x257 paste the 'piece' into it. Then go to image > scale image and knock it down by 1 pixel to have 256x256.
Now save it!
Go back to your checkerboard. Click ctrl+z until your pasted image isnt there anymore. Now, go to your palette and find a red colour. Fill the squares that youve done so your first is the top left. Now fuzzy select the next square, either on the right or directly below, and copy your 2304x2304 image and paste it into it.
Repeat the process shown above in bold, and when youve finished with that square, make it blue. This way you know which parts of the image you have segmented.
For some reason the checkerboard wont create 256x256 for the dimension of 2304x2304.
Obviously you want to do a block of 3x3 in the checkerboard first, and name them something like eye3x3TopLEFT01 eye3x3TopMID01 etc up to 9 different files for each 3x3, to distinguish your files as there will be a 81 files. It will be very easy to lose track if you dont do it this way.
Let me know how you do.