Is there a source that it is an especially auspicious time to daven after completing a mitzva? There are many Yehi Ratzons after fulfilling various mitzvos (shabbos candles, arba minim, etc.), but I haven't found a source for general mitzvos.
While this text is usually read as talking about how to approach prayer, it seems to answer your question as well. Gemara in Berakhot 31a says:
תָּנוּ רַבָּנַן: אֵין עוֹמְדִין לְהִתְפַּלֵּל לֹא מִתּוֹךְ עַצְבוּת, וְלֹא מִתּוֹךְ עַצְלוּת, וְלֹא מִתּוֹךְ שְׂחוֹק, וְלֹא מִתּוֹךְ שִׂיחָה, וְלֹא מִתּוֹךְ קַלּוּת רֹאשׁ, וְלֹא מִתּוֹךְ דְּבָרִים בְּטֵלִים, אֶלָּא מִתּוֹךְ שִׂמְחָה שֶׁל מִצְוָה.
On the topic of proper preparation for prayer, the Sages taught: One may neither stand to pray from an atmosphere of sorrow nor from an atmosphere of laziness, nor from an atmosphere of laughter, nor from an atmosphere of conversation, nor from an atmosphere of frivolity, nor from an atmosphere of purposeless matters. Rather, one should approach prayer from an atmosphere imbued with the joy of a mitzva.
So having done a mitzvah, one presumably has the joy of having done a mitzvah and now is a good time to pray.