IUPAC: Would I prioritize low numbering to highest-priority group, OR try to assign lowest numbers overall?
Very loosely speaking, if your OH group is being named as a prefix, i.e. &quot;hydroxy-something&quot;, then it's no longer &quot;higher priority&quot; than the methyl group, which is itself also a prefix. The &quot;priority&quot; only matters when you're deciding on the suffix, and the aldehydes already occupy that spot.
Yet, that rather informal and unsubstantiated claim probably won't satisfy some readers, and it shouldn't satisfy you, as I could be any useless person on the Internet feeding you false information (which is sadly common). Let's just say that if you had to speak to your teacher about it, you would probably be embarrassed to tell them that &quot;somebody on the Internet wrote a comment that said this&quot;.
So, I will quote a few rules in the IUPAC Blue Book (Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names 2013) which need to be looked at to assign the name. The first step is to decide on the  &quot;principal characteristic group&quot;. The seniority order is listed in Table 4.1, P-41:

1 Radicals
2 Radical anions
[...]
15 Aldehydes and chalcogen analogues
16 Ketones [...]
17 Hydroxy compounds and chalcogen analogues (includes alcohols and phenols) [...]

The principal characteristic groups here are obviously the aldehydes. Notably, P-33.1 states that &quot;only one [suffix] can be placed at the end of a name to indicate the principal characteristic group&quot;, so the alcohol is now relegated to being a prefix, i.e. &quot;hydroxy-&quot;. The next step is to decide on the &quot;parent structure&quot;:

P-44.1.1
The senior parent structure has the maximum number of substituents corresponding to the principal characteristic group (suffix) or senior parent hydride in accord with the seniority of classes (P-41) and the seniority of suffixes (P-43).

Again, it is quite clear that the parent structure here is the chain containing both aldehydes. Lastly, we come to the numbering:

P-14.4
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
[...]
(c) principal characteristic groups and free valences (suffixes);
[...]
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
[...]

(c) doesn't help us resolve the ambiguity at hand, because the aldehydes are at both ends of the principal chain whichever way round we count. So (f) is what matters, and note that it says &quot;all considered together&quot;: it no longer distinguishes between any kind of &quot;priority&quot; between different prefixes. The locant set (4, 21) is lower than the locant set (19, 36), and is consequently the preferred numbering.
If you search Chem.SE for &quot;P-14.4&quot; there will no doubt be similar questions and answers, which may help to clarify the situation with similar examples.
Note that the &quot;lower&quot; locant set is obtained by point-by-point comparison i.e. comparing the first locant of both at the same time, then the second locant of both, etc. until any ties are broken (P-14.3.5). In this case, (4, 21) is lower than (19, 36) because 4 is lower than 19; there is no need to compare the second locants. A common and baseless misconception is that the smallest &quot;sum of locants&quot; wins. This is not true and is not written anywhere in the IUPAC Blue Book.