Here is an edited piece that I wrote years ago; consequently, Thayer rather than BAGD or BDAG is mentioned.
According to Thayer's Greek-English Lexicon, ἐκ (ἐξ) can denote the "origin, source" or "cause" of "generation, birth, race, lineage, [and] nativity" as well as any other type of beginning.
This Greek preposition may also speak of "the efficient cause, or agent from which any action or thing proceeds, is produced, or effected from, or by" (Spiros Zodhiates).
These remarks would indicate that when ἐκ is applied to the Father's activities at 1 Cor. 8:6, it is describing His creative function or his unique act of efficient causation with respect to all things.
It would probably be worth the time to reference the introduction of David Aune's three volume commentary on Revelation. On p. CLXXIX-CLXXX of his introduction to volume I, Aune details the many uses of ἐκ in Revelation. The examples he gives of ἐκ signifying the action of a personal or impersonal agent are: Rev. 2:9; 3:18; 8:11; 9:18. In my humble assessment, 2 Cor. 5:1 is also an example in which ἐκ describes a creation of God--a spiritual building which has a heavenly source.
As for διά, it seems difficult to associate it with the concept of maker or efficient cause in 1 Cor. 8:6 and Heb. 1:2. It is more appropriate to construe its significance as that of intermediate agency:
"Intermediate agency is normally conveyed by διά with the genitive. For example, God delivered the law to Moses by angels (Gal. 3:19) and John sent a message to Christ through his disciples (Matt. 11:2; cf. John 1:3; 3:17)" (Richard A. Young's Grammar, 91-92).