Kitsur SA 46, 9:
אָכַל בָּשָׂר אוֹ אֲפִלּוּ רַק תַּבְשִׁיל שֶׁל בָּשָׂר, לֹא יֹאכַל מַאַכְלֵי חָלָב עַד שֶׁיִּשְׁהֶה שֵׁשׁ שָׁעוֹת. וְהַלּוֹעֵס לַתִּינוֹק, צָרִיךְ גַּם כֵּן לְהַמְתִּין. וְאַף עַל פִּי שֶׁשָּׁהָה כַּשִּׁעוּר, אִם מָצָא בָּשָׂר בֵּין הַשִּׁנַּיִם, צָרִיךְ לְהָסִירוֹ. אֲבָל אֵינוֹ צָרִיךְ לְהַמְתִּין אַחַר כָּךְ, רַק יְקַנַּח אֶת פִּיו וִידִיחוֹ, דְּהַיְנוּ שֶׁיֹאכַל מְעַט פַּת וִיקַנַּח בּוֹ פִּיו, וְגַם מְדִיחוֹ בְּמַיִם אוֹ בִּשְׁאָר מַשְׁקֶה.
... Even if someone did chew meat for a child, he needs to wait, even if he did already wait and afterwards he finds filaments of meat, he needs to extract them, and to wash the mouth e. g. by eating bread and drinking some drink. And there is no need to wait again.
From the above stuff we see that the KSA states that the rule of waiting after meat consumption is not dependent on the amount eaten. If I remember correctly the Haflaa states that if he swallowed the filaments which were between his teeth he has to wait a second time from that time.
In SA those halachot are in Yore Dea 89 (the quoted KSA is from the RMA on sayf 1). There are two reasons that imply a long time meat. The first is the fact that meat is fatty and is adherent and has a persistent taste (the understanding of the Gemara independently of the Chiddush of the second reason, according to the comment of Rashi ), the second reason is the fact that meat is stringy and residues of meat can remain between teeth. The second reason is not linked to amount of meat. For the first it is less obvious.