What is Eldritch Blast's maximum range?

Question

To fulfil a prophecy: What is Eldritch Blast's maximum range? The range I care about is between the Tiefling and the max-distance target at the time of the Tiefling making their attack.

Assuming the following constraints:

• The allowed material is the PHB, DMG, MM, EE, SCAG, XGtE, VGtM, MToF, AC, and the SA Compendium v2.3 and the errata linked therein.
• The setting is the Forgotten Realms, 1492 DR.
• The character is level 20 and conforms to PC rules.
• The character is allowed to multiclass and may indulge in optional rules.
• The character is a Tiefling.
• The character has access to up to 5 major magic items and up to 20 minor magic items (XGtE 135), but not to artefacts.
• The process has to exclude Wish and Gate whether cast by a magic item or not.
• The process has to be reliable (at least 95% of times once during a long rest or more consistently) and reproducible.
• The character is without allies at the start of the process but may create or conjure allies. The Tiefling knows no friendly creature and currently has no familiar.
• The whole set-up has to be prepared within 10 rounds, and Eldritch Blast has to be cast on the 11th round on the turn of the Tiefling, completing the process.

Answer 1

1320 feet

Our Tiefling is a Warlock 2, Sorcerer 3, Trickery Cleric 2, and any class 4.

Warlock 2 gives us the Eldritch Spear invocation, setting the base range of Eldritch Blast to 300 feet. The Spell Sniper feat (from level 4 of any class) doubles that range, and the Distant Spell metamagic from Sorcerer 3 doubles it again, bringing the range to 1200 feet.

At the start of the prep time, we use an action to activate our Channel Divinity: Invoke Duplicity (from Trickery Cleric 2), creating an illusory duplicate that we can cast spells from within 30 feet of us. We spend the next 3 turns using our bonus action to move this duplicate up to its maximum distance from us of 120 feet, and then cast Eldritch Blast as if we were in the duplicate's space, for a total range of 1320 feet.

Other considerations

A DM may allow Eldritch Blast to pass through an Arcane Gate - if they did, we could make our Tiefling a Warlock 11, take that spell as a Mystic Arcanum, and (debatably, given that one could argue we have simply reduced the distance to our target rather than extending the range of our spell) extend our range another 500 feet. However strictly speaking Eldritch Blast is neither a creature nor an object, so would not pass through the Arcane Gate.