The daily map quest provides a steady influx of Alexandrite, even if you take into account the occasional lost fight.
There is no method to obtain a steady influx of Carbontwine, however, unless you're part of a Coil group that divides up Carbontwine drops evenly.
If you exclude Allied Seals, the rate of incoming Alexandrite is nonzero. The rate of incoming Carbontwine is zero. The amount of time to acquire Novus is finite. The amount of time to acquire Augmented Ironworks is infinite.
Spend your seals on Carbontwine, is my recommendation. Also remember that Soldiery Tomestones can be exchanged for Alexandrite maps, and they can drop from FATEs as well. Several ways to get Alex, just one (outside of Coil) to get Carbontwine.
As always, this argument is irrelevant. The purpose behind getting the best gear is not in order be able to accomplish something you otherwise couldn't but rather to accomplish things you can do anyway better and faster. Or, often, not even that - for many, the sole purpose for having the best gear is simply to have the best gear, end of line.
