How should we translate הַנֹּתֵן לְךָ כֹּחַ in Onkelos?

In Targum Onkelos on Ekev, we read:

ח,יח וְזָכַרְתָּ, אֶת-ה אֱלֹהֶיךָ--כִּי הוּא הַנֹּתֵן לְךָ כֹּחַ, לַעֲשׂוֹת חָיִל:  לְמַעַן הָקִים אֶת-בְּרִיתוֹ אֲשֶׁר-נִשְׁבַּע לַאֲבֹתֶיךָ, כַּיּוֹם הַזֶּה.  {פ}

וְתִדְכַר, יָת יְיָ אֱלָהָךְ--אֲרֵי הוּא יָהֵיב לָךְ עֵיצָא, לְמִקְנֵי נִכְסִין:  בְּדִיל לְקַיָּמָא יָת קְיָמֵיהּ דְּקַיֵּים לַאֲבָהָתָךְ, כְּיוֹמָא הָדֵין.  {פ}

This is slightly odd, given that koach in context, in the previous pasuk, was rendered more straightforwardly as cheila: 

ח,יז וְאָמַרְתָּ, בִּלְבָבֶךָ:  כֹּחִי וְעֹצֶם יָדִי, עָשָׂה לִי אֶת-הַחַיִל הַזֶּה.

וְתֵימַר, בְּלִבָּךְ:  חֵילִי וּתְקוֹף יְדַי, קְנָא לִי יָת נִכְסַיָּא הָאִלֵּין.

Shadal notes this and discusses variants:

Thus, in the Lisbon and Anvirsa texts of Onkelos, it has חילא instead of עיצא. And he does not know why in the world there would be עיצא in all the other seforim.

Eitza does have its strangeness going for it, via lectio difficilior. And, if authentic, it could be prompted by the other semantic shift in the pasuk, of לַעֲשׂוֹת חָיִל as לְמִקְנֵי נִכְסִין, acquiring assets, rather than referring to performing feats of military might. And putting insight into the mind of man could then be cast as giving eitzah.

R' Bentzion Berkowitz, in Simlas Ger writes:

Thus, he establishes עיצא as the correct girsa, as a change from cheila in the previous verse. Why? For not with strength does a man prevail, but the counsel of Hashem is what stands for him. Meanwhile, עצה is a Hebrew word, while in Aramaic, it is מלכא. But such is the manner of the translator, when he comes to explain the word word which is the manner he wants it, as R' Berkowitz writes in Oteh Or. And so is it in Targum Yonasan ben Uzien, with the language of מילכא as a translation of עצה. And see in the one who explains his words. (And not like the author of Marpei Lashon Onkelos{?}.}

I would note that עצא is a perfectly fine Aramaic word. Jastrow has an entry, as a Chaldean cognate of the Biblical Hebrew word. Thus:

עיצה , det. עיצתה , pl. עיצן n.f. advice, counsel, council (< H עצה HAL 820; → √עוץ , בר עיצה ; CPA ܥܝܨܐ LSp 85) 1.advice, counsel: sg. עיצא דרמיו deceitful advice FPT Gen 34:13[03];ib. 29:22[05]; עיצה חדה TNGl ib. 11:1; FTV ib.; איעץ יתך עצה TN Ex 18:19 [H איעצך ]; ib. Num 24:14; ונסיבו עיצה ביש{ת}ה they took bad advice TNGl ib. 16:1; הבו עיצה ניסהוד על בריה וניקטליניה give advice so that we can testify against his son to kill him San 23b(60); TNGl ib.; וילפית עצה מן נשיא I took counsel from women VR 620:1 // PRK 148:15; עצתיה דבלעם Balaam's counsel TN Num 31:16; pl. עיצן בישן ib. Dt 32:28 [H עצות ]; Ex 1:10; 15:11; 2.council: sg. בעצתה דקרח ib. Num 26:9 [H בעדת ]; ib. 11; 27:3; בכנישתיהון בעצתיהון in their assemblies and councils TN Gen 49:6

In Beiurei Onkelos, the following insight:

He thus establishes עיצא as primary, the meaning being that He placed in your heart intellectual power and understanding to think of correct plans, to arrive at the purpose of wealth and success. 'Give you counsel' refers to counsel which a person gives to his friend with words; if he wants, he accepts it, and if not, he does not accept it. Meanwhile, continues Bei'urei Onkelos, Onkelos did not translate it as 'gave you strength', for this implies physical strength, which does not always help to success in assets... And לַעֲשׂוֹת חָיִל refers to assets, rather than prevailing in battles, because the conquest of the land was via miracles and mightiness performed by Hashem...

Practically, though, the battles were often waged by the people. Still, I agree that the shift in meaning of laasot chayil is likely connected to this choice of eitzah over cheilah.

The only other possibility which occurred to me was that there was some textual corruption in play. The צ can look similar to a ל in some scripts, and perhaps some other mangling occurred with the ח and ע. Or maybe this was a corruption off of some form of the word עוצם, strength, like עצמא. But I do not have any texts to back it up, and the context supports a semantic shift in Onkelos, as discussed above.