I7 6700k - High Temp issue

I have a gaming build which is close to four years old now (built it in 2016).

CPU - Intel i7 6700k @ 4GHz. Turbo upto 4.2 GHz (no overclocking)
GPU - Zotac GTX 970 (no overclocking)
CPU Cooler - H100i GTX
Motherboard - Asus E3 Pro Gaming v5
BIOS version - 2606
Case - Corsair C70 Vengeance (lots of openings for airflow)
Fans - 5 [2 intake and 3 (2 AIO radiator+1 rear) for exhaust ]

Of late, I observed quite high idle temps on my CPU (close to 60c with random spikes up to 85c), while gaming (Arkham Knight, GTA V, Alien Isolation) it would shoot up to 90c and occasionally hit 100c (never had an automatic shut down though).
I hadn't replaced the stock thermal paste which came with the H100i GTX in all these years. So the first thing I did was replace the stock thermal paste with the Arctic MX-4 2019 edition and for good measure cleaned out the case, air filters, fans and the radiator fins. I even replaced the stock thermal paste on the GPU with the Arctic.

Although my idle temps have come down from 60c to hovering around the 45c-50c mark (I think this is high for idle), I can still see spikes of up to 85c.

Playing Batman Arkham Knight on Ultra ( with PhysX turned on) yields sustained temps of 85c-87c with spikes of up to 100c on the CPU and the GPU stays close to 80c but never exceeds it. Running even a simple stress test such as the CPU-Z bench for 10 mins gives sustained temps of 95c-100c at 100% load. I didn't bother with Prime95. Motherboard temp is at 41c. I live in India where the climate is warm. The ambient temperature is usually around 30c in the monsoons and can even hit 40c in summers (I have an air conditioner in the room but I don't run it all day long). Could this be a contributing factor?

At first, I thought I had botched the thermal paste application but since then I have cleaned and re-applied the same (dot method) at least 6 times with the same high temps. The cooler pump is working fine and so are all the fans.

I am at my wits end as to how to proceed with this. I have ordered the Noctua NT-H1 as a back-up because the Arctic is only good for two-three more applications.

I would like to hear some suggestions from you guys.
Does the i7-6700K usually run at high temps?
Is the Arctic MX-4 any good or should I use the Noctua NT-H1?
Should I opt for air cooling (Noctua NH D15) instead of AIO? (getting the CPU block to mount is a ***** due to the thick tubes)

P.S. I know, too many questions. Apologies!