The Theurgy Wizard from UA: Wizard Revisited gets to choose a Cleric Domain at 2nd level. At 14th level they get the Arcane High Priest feature, which grants them the 17th-level benefits associated with their chosen domain.
A cleric who chose Arcana as their domain would therefore gain the Arcane Mastery feature, which reads as follows:
At 17th level, you choose four spells from the wizard spell list, one from each of the following levels: 6th, 7th, 8th, and 9th. You add them to your list of domain spells. Like your other domain spells, they are always prepared and count as cleric spells for you.
I've seen people on the internet argue that this 14th level wizard would be able to cast the chosen 8th and 9th level spells. This is of course not true, as the wizard in question would not have the necessary spell slots, regardless of whether those spells are always prepared.
But this wizard could pick up three levels in another Full Caster class (bard, cleric, druid, or sorcerer) or six levels in a Half Caster class (paladin, ranger, or this new UA revised artificer). Per the Multiclassing Rules, this would give this character a 9th level spell slot.
Question: Can this hypothetical character cast their 8th and 9th level spells granted by the Arcane Mastery feature via the Arcane High Priest feature, despite not being able to know or prepare any other spells of that level?
Disclaimer: I know that UAs are playtest material and not tuned for multiclassing. I know that the situation I describe in this question is very unlikely to come up in a real-life D&D game. I'm interested in an answer per RAW. I really like designing (sub)classes, (sub)races, feats, magic items, etc. for my game. So I need to know how the D&D 5e rules behave under extreme circumstances, hence this convoluted question.