How can I cope with small internal pull-up resistors on an I2C bus?
You can use an I2C bus extender which can act as a buffer in between the two devices.

http://www.nxp.com/documents/data_sheet/P82B715.pdf

These devices may have other names as well, like I2C bus "line buffer".  They're made by a variety of manufacturers (TI and NXP come to mind).  Pick one that fits your needs.