Fastest way to move from F1 to H4/H4 EAD

I am currently working on F1 STEM OPT extension which is expiring on 5th June, 2019 and my husband is on H1-B with an approved I-140 for green card. My H1-B was filed this year in premium but I haven’t heard if my application was picked in the lottery. If my application is not picked in the lottery this year, I will have to move to H4 and H4-EAD to continue working in the US. So, in my case, what will be the best and the fastest way to get converted to H4 and obtain a H4-EAD. I know I can file both together and go on a leave of absence at my job till I receive my EAD. And the estimated timeline for this might be 5-6 months. So is there any better way to move to H4 and H4-EAD with the least period of absence from my work. I was suggested to just re-enter US with a fresh H4 and then apply for EAD once I am in the country. But I don’t know if this will be faster and if it will work. Please advice. Thanks in advance.

Who ever advised the re-entry option, thats the workable best.
But there is another (not guaranteed) option could be.
File H4+EAD ASAP, get a letter of potential termination (due to the legal employable status issue on your OPT expiration), take an infoPass appointment and explain the financial hardship with the help of the manager’s letter at the infoPass appointment. They may(not guaranteed) escalate the case as a special case. This would better work if you use both above solutions together(exit and enter with H4, apply EAD and go for infoPass). Good luck. (but check out if your current pending H1 may get impacted as you are requesting another (F to H4) Change of Status while your quota COS (F to H1) is pending.

Thanks @ImmiGeek for the prompt reply.

I haven’t heard about my H1 being picked yet. I just wanted to understand the options I had. Looks like re-entering US with a fresh H4 is the best option for me considering the least leave of absence from work.

Thanks Again.