Headphones - help!

I cannot stand the sound quality from the built in speakers and need go find an alternative.

I have tried my Sony WH 1000XM3 but they don't fit over the BoboVR S3 Pro strap and I feel like most over ear headphones probably won't. Furthermore, I tried some wireless JBL in ear headphones over Bluetooth and experienced a lot of sound latency - never experienced this on any other device with these before.

My questions:

What headphones can I use to avoid the sound latency? Would prefer to use the 3.5mm jack rather than the USB given I have the S3 Pro which uses that port although it's not a total deal breaker as sound quality is definitely the priority for me.

Have you come across any over ear headphones that fit with a bulky headstrap? I seem to see a lot of recommendations for over ear but I don't understand how people are using these!