Diligence is cheaper:
200k in Silver + 5k in things = ~45 silver plates + 500 diligence per day
3 super moos = 300k
45 silver plates = ~8000 smithing mastery via quality arrows (I did this, got to level 6 + 2000 mastery) = ~1/3 of the total to level 10
Each level 10 smithing = 2555 diligence, so that's ~1/3 of the diligence for this
total cost: 505k + 200k worth of leveling up = 700k to 1300 diligence. Really it's only about 600 the first day, then 800 the second, and 2500 the third, but that's ok.
72 days of doing this would cost ~50mil and get you there.
If you want to do it in less than 72 days, you don't get the 500 diligence per day - 1.1mil for supermoos + silver => ~800 dill, 121 times that = ~150 million to do max diligence (from nothing) in one day. 110mil of that cost is for Super Moos, so yeah, you save a lot of money by not using them.
Also you get some arrows, and 1000 mining mastery - so every 23~ days you max out mining and get +2555 willpower, for a total of 7500 willpower along with your 97000 diligence. (that's level 24 Willpower, if you had none to start with)
The automation makes it much quicker, just divide exp to next level by exp per stack of arrows, put it in, and afk a bit. You can probably expect a 4-5% reduction in total time due to double mastery, with a caveat - if you automatically do a stack of crafting, it does not stop when you reach the mastery necessary to level up and you do not get the mastery from any more crafts, so unexpected double masteries don't help if you overshoot. It's probably a good idea to undershoot (input 90% of the amount necessary to levelup) and then step the rest of the way using single crafts if you care about money. If not, well, you're only saving about 3 days and 3mil anyway.
It might be more cost effective to use Adamantium and forge Strong Arrows, I haven't run the numbers - you'll get more mastery (at level4+ smithing) which means fewer fatigue pots, but spend 5x as much on ores.