I think that it is just a matter of irregular spelling, or possibly inaccurate transcription from different sources, some of which are hard to decipher, rather than anything really weird.
At Livy XXV.9 we find Cornelius lustrum condidit : censa sunt civium capita centum quadraginta tria millia septingenta quatuor. Livy appears to use either milia or millia at a whim.
Editors differ in their approach to Livy (and others!). Some 'correct' everything according to their own ideas : for instance, one may allow the recorded variations in the word, while others prefer one form only. The words septingenta and quatuor can appear as septinginta and quattuor. A brief Google search through different collections will show up this variability, though I really do not think that there is anything significant to be gained by pursuing the matter.
You might, in fact, ask a general question about how and why the accidence of cardinals differs. Unus, duo and tres are declinable. From quattuor to centum they are indeclinable. Hundreds upwards from ducenti to nongenti are declined as for -o and -a stems. Then comes the word in which you are interested. Mille (sometimes mile) is, as you say, usually regarded as an indeclinable adjective, but has a corresponding plural milia (or millia) which is declinable, as if a substantive of the third declension, similar to maria and cubilia, the plurals of mare and cubile. The fact that mille is thought of as an indeclinable singular adjective, while milia is undoubtedly a declinable plural noun is probably a fact of grammarians' usage, rather than unexplained divergent accidence : just as, in English, we have such expressions as many thousand miles and many thousands of miles — essentially the same, but used idiosyncratically — though we are content to accept either without a need to explain the reason for the difference.