Arcane disciple and archmage spell-like abilities

[Mister Freeze]

At first I agreed with the interpretation that you could not have a spell obtained from arcane disciple be a spell-like ability, but now I'm now not so sure.  It specifically says the spells granted by the domain become arcane, so that isn't the problem.  The issue is the line:

"Each day, you may prepare (or cast, if you cast spells without preparation) a maximum of one of these domain spells of each level."

Relevant archmage text:

"An archmage who selects this type of high arcana can use one of her arcane spell slots (other than a slot expended to learn this or any other type of high arcana) to permanently prepare one of her arcane spells as a spell-like ability that can be used twice per day."

You're only preparing it once, and casting a spell is not the same as using a spell-like ability. 

Am I clutching at straws here?  Would this ever fly?  Straight yes or no to this last bit please.

[X-Codes]

Seems like you can do it to me.  Honestly, I think that's one of the weaker Archmage picks unless you do something like this, so yeah.

[Mister Freeze]

Additional question:
"If spell-like ability is selected more than one time as a high arcana choice, this ability can apply to the same spell chosen the first time (increasing the number of times per day it can be used) or to a different spell. "

Does this mean if I take spell-like ability twice on the same spell, I would be giving up 2 5th level slots, and only one 9th level slot, in the case of miracle?

[X-Codes]

No.  You'd have to give up another 9th-level slot, and arguably you can't do that twice for Miracle since, the way the ability is worded, "you permanently prepare [Miracle]," and you can't prepare Miracle more than once according to the restrictions of Arcane Disciple.