Hi @Judicaël_Ihorim
I've had came to same situation earlier. Technically speacking there is no alternative when you migrate the properties from DTM to Launch. The "development" flag only available at the time of creation of new property.
But yes there is other alternative I've tried. You can create new development property for your private extension and then once you installed private extension in newly development property - the same extension will be available in other properties too respective to their extension catalogue.
This way you can ready to use your private extension in migrated properties.
Hope this helps.
Thanks