No...Head-of-Household is for people who have an actual dependent to take care of...like a minor child, aging parent, or another relative, who has little or no income, and for whom you supply more than half their support. A "spouse" is never a dependent. So based on what you've posted so far, neither of you can file HOH.
MFS is also not likely helpful, but you can test it if you want, but next January, just buy the Desktop Software that downloads to your home computer. That way you can test both MFJ and MFS situations...since Desktop software lets you prepare as many tax return files as you want....then file only when you have made your decision.
You could buy the desktop 2017 tax software now to test it using your 2017 data and the "What-IF" worksheet, but then you'd have to buy the 2018 software to actually prepare the 2018 tax return next January anyhow (every year's software is unique), AND all the 2018 software changes may not be reflected in the 2017 software, as not all of the effects of massive 2018 changes are clear yet. You don't need to decide until Jan-March of 2019 anyhow.
You cannot do that with the Online software, and switching and Online file back and forth form MFJ to MFS can mess up the files in strange ways and give you confusing/improper results.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*