Sadly there is no way to cover those textures with CC licenses. CC licenses allow 3rd party distribution while their license is specially crafted to stop the distribution by others. However, you may post your model untextured and give link to the texture. This way, your model remains CC licensed while anyone needs to use it can just download and use it. However, this will not be possible for CC-By-SA since SA requires him to redistribute textured derivative using the same license, which he cannot.

PS: It doesnt matter what the license you are converting to says, if the current license does not allow, then its not allowed.

http://webtreats.mysitemyway.com/terms-of-use/ makes it clear that re-distribution is not permitted, but for something to be freely licensed, it has to permit such use. The owner can be contacted and asked to use ccby3 or ccbysa3 for example, for making it easier to know to users what is permitted (because cc licenses are widely known - even if most people never read the license text but just the description, which I am not criticizing).

"Legal Stuff" in the footer of http://texturemate.com/ claims that ccby3 is the license but it also says "The only exception is that they cannot be redistributed commercially in their unedited form.", which is a contradiction to being ccby3 licensed. The owner should be contacted and asked to either remove the restrictions or offer them that they instead write that for 1:1 redistribution attribution *is* required, which would be the default for ccby3 anyway.

You can find a discussion that resolved a ccby3+restrictions situation successfuly on FGD forums: http://forum.freegamedev.net/viewtopic.php?f=6&t=3088

A similar situation exists on http://textures.cc/, where they say "please do not redistribute the collection of images", which can probably be ignored. I did point that issue out to them... kind of... via twitter: https://twitter.com/qubodup/status/214237221228781568 It seems they decided not to change the text.

When in doubt, the safest solution is to ask the owners (hosts) of free to use media, whether they are ok with you uploading INSERT WORK URL HERE to http://opengameart.org under the INSERT LICENSE URL(s) HERE. If they allow it, you should include a text describing how you were given permission (email? telephone? forum? twitter? with quotes/links if possible) in your upload. In both negative and positive responses you can share the reaction here in this forum so others can find the information.

Cheers!