If I got you correctly, you need to migrate just data from a production one database to a development database, and you might have to repeat that process a few times. So as long as you implement the migration in a repeatable, idempotent manner, that should be not much of a problem. The most simplestsimple solution might be to clear all previously migrated data from your development database before a new migration, but you might not be happy with that due to performance reasons, or because you have some data in your development database which might be kept there. If that is the case, you will have to design some synching mechanism between those two database, or at least a mechanism to keep or recreate the data in the development DB you do not want to be deleted.
What I cannot tell you is if fiddling around with the time stamps of your migration table will be a problem - for this one needs to know the gory details of your framework.