If you don't act over-pessimist with that "1x vs 2x" comparison, management only sees that you offer two valid options and the second one takes double time for no reason. So obvious, take option 1.

Maybe you can propose to hack the code in an accumulative +1x time from the previous hacks (thus making it clear that next hacks will take more and more time), or design it into the system with a nice and constant 2x. That could be a strong indication for management that the hackish way does have a long term cost.