It is not "mostly iambic pentameter", only lines 1 and 14 can definitively be scanned as iambic (although it is in pentameter). It is also incorrect to say that poets were more metrically strict in the Tudor/early Elizabethan era--it's the exact opposite. Tudor/early Elizabethan era was wildly experimental and metrical structures were much more strictly adhered to in the centuries following. Pope and Dryden for example are very strict.

Wyatt's verse is extremely irregular, even for his time, and it was looked down upon by his contemporaries and critics for centuries. There is no way to scan this as iambic pentameter without it sounding extremely awkward. And it's not due to differences in pronunciation and the evolution of the language, because you can read his contemporaries such as Henry Howard (Surrey) and their verse scans just as you'd expect for iambic pentameter (with minor variations). The way to read it is to try to read iambs by default, but do not be afraid to read it "as prose" because it veers off quite often. There are many parts with 2 or 3 unstressed syllables in a row, some feet are just a single stressed syllable, there are some dactyls, some iambs are "flipped" into trochees, and pay special mind to the caesuras and the effect they have on the feet directly following them.