The chronological problem in the saving of Moshe

The following chronological difficulty struck me (ouch!) when reading through parshat Shemot. The pasuk states:

ה  וַתֵּרֶד בַּת-פַּרְעֹה לִרְחֹץ עַל-הַיְאֹר, וְנַעֲרֹתֶיהָ הֹלְכֹת עַל-יַד הַיְאֹר; וַתֵּרֶא אֶת-הַתֵּבָה בְּתוֹךְ הַסּוּף, וַתִּשְׁלַח אֶת-אֲמָתָהּ וַתִּקָּחֶהָ.

5 And the daughter of Pharaoh came down to bathe in the river; and her maidens walked along by the river-side; and she saw the ark among the flags, and sent her handmaid to fetch it.

Regarding this last point, וַתִּשְׁלַח אֶת-אֲמָתָהּ וַתִּקָּחֶהָ, how could she have sent forth Amasa? After all, we know that Amasa lived hundreds of years later, at the time of David and Avshalom:

כה  וְאֶת-עֲמָשָׂא, שָׂם אַבְשָׁלֹם תַּחַת יוֹאָב--עַל-הַצָּבָא; וַעֲמָשָׂא בֶן-אִישׁ, וּשְׁמוֹ יִתְרָא הַיִּשְׂרְאֵלִי, אֲשֶׁר-בָּא אֶל-אֲבִיגַל בַּת-נָחָשׁ, אֲחוֹת צְרוּיָה אֵם יוֹאָב.

25 And Absalom had set Amasa over the host instead of Joab. Now Amasa was the son of a man, whose name was Ithra the Jesraelite, that went in to Abigal the daughter of Nahash, sister to Zeruiah Joab's mother.

The answer may simply be that ain mukdam umeuchar baTorah. Or maybe not. Suggestions?

(Another problem, of course, is vatikacheha. Maybe this is acceptable under shlucho shel Adam kemoso.)