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.