I know this is an old post, but could prove useful to others searching on the topic...
Now I just ran into a similar issue, and the only way I could get around altering the resolution was to resample the data. This had to be done at the tile level, and with almost 5000 tiles it could have been time consuming.
I just created a toolbox>model Used the Iterator Raster function from the dropdown on top and built my model to iterate all raster tiles, then send each one to the resample tool. This allowed me to set the cell size (x,y) for each tile. BE AWARE of the reference system... The first time I ran my model I didn't realize the tiles were in stateplane FEET and when I wanted them in METERS for my end result, I just typed in (1,1) for cell size. Not realizing that my end product produced (0.3048,0.3048) meter cell sizes... I had to delete it all and start over.
If anyone actually sees this as useful and wants to learn more, post a comment and I can add screen shots of models as examples.
NOTE: when using the iterator in model builder, you have to include a recursive name to the output, such as %name%... otherwise the model will run, the first tile will be processed and it will time out thinking the next tile has the same name as the first and will have no where to save its output.