There is an alternative to porting Qt to iOS and Android - port them to Qt. To clarify, if Qt contained abstraction veneers and perhaps a bit of help from moc (or a new preprocessor) to provide substantial iOS and Android support in generic code then when you intend to write a portable mobile app you make an effort to use those veneers and preprocessor functions and a small subset of "proper" Qt. On a desktop system, those veneers just translate to the "proper" underlying Qt classes, but on mobile devices they translate to suitable iOS and Android calls. Veneer source-code suitable for use in the iOS and Android SDK would be provided for inclusion in ports to those systems.

You would not be able to just cross-compile to another platform (partly because of language incompatibilities, device differences, and licensing restrictions) but hopefully the porting and maintenance effort might be reduced to mostly cut-and-paste and minor patching. I know it's not ideal, but considering the difficulty of providing the alternatives might it not be a possibility?