Do any of these sources of AC bonuses conflict or negate each other?

Question

My understanding, confirmed by the answer to this question: When a War Caster Wizard carrying a shield casts the spell "Shield" does the AC bonus Stack? is that anywhere an actual +N bonus to AC is listed, they all stack.

So does the following work, or is there some conflict between some of these that would not allow them to be used together?

Barbarian 1 / Cleric 1 / Wizard 5

Unarmored, with a shield. Con 18, Dex 15

• Base AC is 10 + 2 (dex) + 4 (con) = 16
• Shield (+2 AC) raises this to 18

Casts Haste as an action and Shield of Faith as a Bonus Action (a house rule allows 2 concentration spells):

• Haste gives +2 AC, for AC 20
• Shield of Faith gives +2 AC, bringing AC up to 22

If she ever gets hit, cast Shield as a reaction:

• an additional +5 to AC bringing AC up to 27 for one round

I know all of these would stack, but does anything prevent them from all being used together?

Answer 1

You are almost exactly correct.

All the math you have is accurate. However, you've missed a subtle rule mentioned in the PHB (pg. 202) regarding spells cast as Bonus Actions. Namely, when casting a spell as a bonus action

You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

Thus, while it is possible to reach 27 AC using the methods you've described, you cannot cast Haste and Shield of Faith on a single turn.