Beshalach: the sanctuary, O Lord, [which] Your hands founded

Within Az Yashir, we encounter {Shemot:15:17}:

יז תְּבִאֵמוֹ, וְתִטָּעֵמוֹ בְּהַר נַחֲלָתְךָ-- {ס} מָכוֹן {ר} לְשִׁבְתְּךָ פָּעַלְתָּ, ה; {ס} מִקְּדָשׁ, אֲדֹנָי כּוֹנְנוּ {ר} יָדֶיךָ. {ס

17 Thou bringest them in, and plantest them in the mountain of Thine inheritance, the place, O LORD, which Thou hast made for Thee to dwell in, the sanctuary, O Lord, which Thy hands have established.

Rashi comments on this:

the sanctuary Heb. מִקְּדָשׁ. The cantillation sign over it is a “zakef gadol,” to separate it from the word ה following it. [The verse thus means:] the sanctuary which Your hands founded, O Lord. The Temple is beloved, since, whereas the world was created with “one hand,” as it is said: “Even My hand laid the foundation of the earth” (Isa. 48:13), the sanctuary [will be built] with “two hands.” When will it be built with "two hands"? At the time when “the Lord will reign to all eternity” [verse 18]. In the future, when the entire ruling power is His. — [from Mechilta and Keth. 5a]

What was the other option, which Rashi is excluding? Well, zakef is a disjunctive accent, separating from the word following it. Without it, it would be mikdash-Hashem, "Hashem's sanctuary your hands have established."

We can see this visually. Note that both tipcha and zakef act to divide a phrase in two where the phrase ends in a silluk (and sof pasuk) and so where you have both, the zakef, the earlier one, must subdivide first (or else the zakef makes no sense, not splitting a phrase ending in silluk). There is a zakef on mikdash, and a tipcha on the next word, Hashem.

Thus, we get:

A sanctuary || Hashem your hands have established
where the second phrase is then broken up into
Hashem || your hands have established

Shadal has an interesting suggestion relating the zakef gadol of mikdash with the dagesh in the same word (such that it is miqqedash):

מקדש : דגש הקו"ף לתפארת הקריאה, ונ"ל ששמוהו כדי שיהיה השוא נע, וזה כדי להרבות הברות התיבה, וזה כדי שיהיה נשמע יותר ניגון הזקף הגדול

"The dagesh in the quf is to beautify the reading {and does not imply a different meaning than mikdash} and it seems to me that they placed it there so that the sheva would be na {rather than nach}, and this is turn is to increase the pronunciation of the word, and this is so that the zakef gadol's melody would be heard more."

The trup, though, is marking that clarifies ambiguous parsings. Is there anything in the pasuk itself we can muster as evidence towards this parsing?

I would suggest that the principle of Biblical parallelism can reinforce this parsing. After all, Az Yashir is a song, and Biblical songs typically display Biblical parallelism. The pasuk, again, is:

תְּבִאֵמוֹ, וְתִטָּעֵמוֹ בְּהַר נַחֲלָתְךָ-- {ס} מָכוֹן {ר} לְשִׁבְתְּךָ פָּעַלְתָּ, ה; {ס} מִקְּדָשׁ, אֲדֹנָי כּוֹנְנוּ {ר} יָדֶיךָ.

The parallelism is: מָכוֹן לְשִׁבְתְּךָ פָּעַלְתָּ ה || מִקְּדָשׁ אֲדֹנָי כּוֹנְנוּ יָדֶיךָ
Thus, מָכוֹן לְשִׁבְתְּךָ parallels מִקְּדָשׁ
פָּעַלְתָּ parallels כּוֹנְנוּ יָדֶיךָ
YKVK parallels Adonai

Thus last parallelism and rewording is not so obvious, since we don't pronounce YKVK as such nowadays, but rather as Adonai, so it sounds to us like it is identical. But in reality, it is a standard parallelism with the second part rephrasing the first part, usually serving the same function. Thus, we bolster the parsing marked by the trup.