Do you know which 18-200 version? The OS or non-OS version? If its the OS version and has the High Speed Motor variant, be sure that it is has the AF/Man switch firmly set to the right choice. I have seen several OS lens (different manufacturers) play tricks when the switches for AF/Manual is not firmly set. If you also switch the OS selector back and forth a few times to be sure it is making good contact!

If you have the non-OS/HSM version check with Sigma Service to be sure that you have a new enough chip version to work with those two cameras. They will re-chip for free if the lens was purchased through an authorized dealer.

Sigma is doesn't really reverse engineer like some of the third party lens manufacturers. Sigma has had contracts with Canon and Nikon to produce compatible products and thus had access to the full spec of the interface.

A link you may find helpful

Sigma Photo Service & Support

Let us know how it works out. I've used Sigma lens in several different mounts and with different bodies with little or no trouble other than two I've flooded in pouring rain.