Very good question.
I think you should be deducting the Schedule E expenses on line 2 of form 1116. That would address your valid concern. Those Schedule E expenses are "definitely related" to the foreign gross income.
Even if you get beyond this be aware that the Part III credit calculation limits the foreign credit to
your total US tax liability * (your foreign income / your worldwide income)
for those with small foreign income, that ratio is small. because US taxes are often so much lower than foreign taxes, you are not likely to "get back" the foreign tax. Rather what is happening is that you will not be paying to the US what the US would have taxed you (usually less than the foreign government).
re: line 2 see the 1116 instructions and its further references as you wish, page 17
https://www.irs.gov/pub/irs-pdf/i1116.pdf
which says:
Line 2
Enter your deductions that definitely relate to the gross
income from foreign sources shown on line 1a. For example,
if you are reporting foreign business income on line 1a,
include on line 2 business expenses such as supplies and
advertising incurred as part of operating the foreign business.
Also include on line 2 state and local income taxes related to
foreign source income. For more information, see Pub. 514
and section 861 and the regulations under that section.
Attach a statement listing the separate expenses included on
line 2.
Don't include any interest expense on line 2. See lines 4a
and 4b for special rules for interest expense.
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