Hi @nehaj
H4 stamping outside USA
Going out of US and getting H4 visa stamp is the fastest option for you to get on to H4. Once you are back, re-apply H4 EAD and you will get EAD card in about 3-4 months.
I have covered multiple scenarios of travel while H4 EAD is pending here.
Parallel H1B transfer
You can file an H1B transfer too while your H4 COS is pending but it will create status issues based on which one gets approved last.
If you want to stay on H1B, i suggest to file H1B transfer in Premium and start working on receipt.
If you are okay with H4 EAD, then go out and get H4 visa.
More scenarios for H1B 60 day grace period.