Shields work perfectly fine on multi hit tankbusters. They're not like Sheltron where they fade after one hit no matter how much damage it does. A 10k shield reduces the same amount of damage whether it's used on a single 60k hit or 6 10k hits. A Rampart on that same damage would reduce damage by 12k total. The only real difference is that the shield mitigates all up front and pretty much negates one hit completely, while other cooldowns reduce much less on each hit but the damage reduced adds up over time.
Using your A7S example, TBN would be really good there. A TBN by itself could probably reduce one of the attacks to 0 (with some shield left over for the second hit), so you wouldn't get that stack of vuln up. Combined with Adloquium and Stoneskin, you would have been able to completely avoid 2 or 3 stacks which would reduce the damage from the last 3 hits.
