F1, H1B are two completely non-immigrant status. TPS is not a status at all, you are protected temporarily to remain in US as long as it is valid. Since your current status in F1, once your TPS is terminated, you can go back to F1, if you maintain F1 status until then.

Now, you are applying for H1B in April. Given that your H1B is approved, your latest status will be H1B, not TPS. So, you can travel outside the country on H1B itself and get stamped.
There are administrative process that takes much longer time to approve H1B stamping and I would recommend go to Nepal and stay with family and still could able to work remotely. However, internet bandwidth might be a problem. OW you can go to Canada or Mexico, but if you got stuck, and have to stay in hotel, you send lots of money.

Going to stamp H1B with TPS advance parole ? Do you think, this works? Why are you making life complicated ? I know you try to act smart, just in case if H1B is denied , you get a privileged of returning on TPS. I do not think H1B stamping will be denied unless you were out-of-status earlier. Hope this helps, however, do consult a good lawyer before you make any decision. H1B stamping need to be planned and prepare lots of documents.

Nepalinajar, it is very important to have an approved (not pending) advance parole before you depart the US. Without approved AP your tps application/approval will be considered abandoned. You can apply for it at any time. Even If your h1 is approved, stamped I'd suggest you to maintain tps. Always be on safe side!

neerman, H1B doesn't start until October 1st. So technically applicant will not be in H1B status until October 1st even if it gets approved in advance.

But there used to be something called - CAP-GAP rule which used to apply to F1 in OPT. Not sure if this is valid to TPS EAD.

NN, you have not mentioned any dates of your F1 (expiration is valid I-20 date) and TPS EAD expiration.

Not sure why you would need advance Parole as long as you have valid F1 status. Even with advance parole there is no guarantee that applicant will be allowed to enter USA freely, It is still in the discretion of US Customs.

Also, remember since H1B only starts from October 1st, many times lawyer advise not to enter USA even with H1B stamped visa way in advance. A month or so is ideal but any period longer than that is still risky.

1st I would ask employer/lawyer what is the reason for not applying COS, rather doing consular processing? They should have a valid reason.
2nd make sure you have authorization to work until the start of H1B.

Look for PP option. USCIS stopped PP while back for few (6) months and not sure if they started PP again.

I do not see any issue with your case as long as you were in status and have valid work authorization to work until the start of H1B.

And finally, H1B visa are the easiest as long as you can prove that their is employer -employee relationship and both are in good standings. And BTW, they cannot deny visa because of immigrant intend because H1B is classified as dual-intent visa category.

Always consult with Lawyers. very important..usually they charge you $50-$100 for 1/2 hours initial consultant. Do not always trust employer lawyer. Consult with outside.

Thank you everyone for your valuable comments. Today, I talked with the immigration adviser from my company and the lawyer from the company who is filing my H1B in coming April. I convinced them that I have never ever been Out-of-status in my entire time within united states and filing H1B with change of status strategy would be better option for me as I do not have to travel outside of the country. I also mentioned them the risk associated with it. Finally, they agreed with it and planning to apply the H1B petition with 'Change of Status' strategy.