I guess I am missing something here.
Why do you think you need to get the visa and or visa stamp? Let me state this again. Just to make sure you understand correctly.
If you are approved for an H-1B visa, there will be no need to depart the U.S. and re-enter on a visa to remain in the U.S Your attorney would include a change of status requesting new I-94's. You will get New I-94's indicating you are "in status" as an H-1B.
If your current H4 is expiring, you can have your attorney file to extend status, and get new I-94's all without departing the U.S. You can remain in the U.S. until the extension is approved or denied.
October 1, is not sacrosanct in terms of visas in your circumstances. you do not have to get your visa stamped, because you would have changed status in the U.S. and you would have new I-94's indicating you are present in H-1 status. You can change status from H4 to H-1 without departing the U.S. There is no need to get a new visa in your passport until you travel the next time. So the only reason to do depart and re-enter in status in terms of the visa in your passport is to avoid delays on future trips. So essentially you can depart the U.S. to re-enter at any time after the approval. It does not have to be on that date. (October one is sacrosanct as you say with respect to the start date of your work status in relation to the start date of employment. The petitions filed on April 1 are for jobs starting on October 1)
The H4 extension would not impact your H-1. If the H-1 is approved, then you would get new H-1 I-94's with a begin date, and on that date you would no longer be in H4 status,you would be in H1 status.
Yes you can apply for an H4 extension on 1 may if the H1 was not approved. BUT you would not have to. Some attorneys would advise you that you can wait until the H1 is approved or denied. But in your case I would recommend extending the H4 as soon as you can, if your H1 has not been approved.
in response to your itemized concerns:
1. apply for H1B YES
2. Apply H4 YES, but follow your attorney's advise on this.
3. Wait YES
4. Overstay....NOT an issue. Remember, if your attorney does it right, then you can get new I-94's while in the U.S. You do not have to depart unless you want to for convenience purposes.
5. See number for. Will work if that is what you want to do