Clair's website features an academic take on the tanaga and the haiku. Do check it out in this link. Here's an interesting quote:

However, it should be noted that the definition found in Juan
de Noceda and Pedro de Sanlucar's Vocabulario de la Lengua Tagala, it did not
that the tanaga is a monoriming quatrain, but the form is stated as composed of
seven syllables (per line), and has four lines (Manuel 1972?).

If this is so, then modernizing the Tanaga by dropping the perfect rhyme, or rhyme altogether is actually a movement toward fulfillment of its (possibly) original form. Most popular tanagas have a rhyme on the last syllable - a feature quite common in other forms of Filipino poetry. While I do not have evidence to point out that internal rhymes were used in tanagas, it is not entirely irresponsible to surmise that they were utilized, at least among the oral tradition, or in the ancient tanagas themselves.

The Filipino language and its regional counterparts have certain elements which makes me want to believe that such a case is very possible. Consider the nature of the vowels themselves in the ancient Filipino syllabication in the baybayin/alibata:

The vowels "e-i" and "o-u" are regarded as interchangeable sounds. The same goes for the consonants "d" and "r"; they are considered to be interchangeable sounds. The liaison between words, and substitution of the consonants "m" and "n", or "p" also seem to support this idea
that with such mechanics in the language itself, it is not impossible that internal rhymes are formed on purpose - especially in a predominantly phonetic or short "a" language like ours.

Furthermore, all these phonetics I've mentioned have remnants which exists and remain noticeable to this day when Cebuanos and Visayans, and other provincial citizens speak the language. This is also noticeably a common accident among students who have Filipino as their second language, as far as I've noticed it.

All these seem to point that it is not a remote possibility that internal rhymes are inherent characteristics of the language itself. While it cannot be categorically stated that they were exploited and used to the advantage of ancient Filipino poetics, it does seem show that it is not entirely difficult to consider it being applied.

I hope a more scientific study is made on this matter. If there exists one already, please email me and let me know.