As far as I know, Y-Browser is the only file browser at present that provides the functionality and I have the same problem you described while copying files larger than 15mb.
However, a light at the end of the tunnel could be the new file browser by Lonely cat games. I think its called X-file or X-plore or something and still in the beta, which is temporarily free. I have'nt tried it personally but i read somewhere that it reads the inbox. You could try that.
If, you are using PC-Suite, you could browse to the desired location on your memory card and copy it these. I think it takes the same amount of time.
Good Luck.