Some clarification here.
As a standard, boilerplate practice the City will write up an illegal basement conversion for de-conversion. This however does NOT mean that you have to de-convert. There are options and variables. The City can require you to remove anything that was built without permits. However, if you negotiate with City attorneys and are able to show that what was built is compliant they usually won't play hardball unless you give them a reason to.
If you can get an architect to draw up the space for compliance and get a permit, then you can avoid de-conversion. There are however numerous requirements such as ceiling height, egress, vent and light, electrical, plumbing, heating etc. Zoning also plays a big part.
If you look on your violation list they probably wrote up a 002011 number for plans and permit and a 110 series for the de-conversion. My recommendation is that you hire an attorney to represent you and also an architect or inspector to assess your construction options. I have a good attorney for such matters listed on my website.
You can email me the violation list and I'll take a quick look at it for you. Did they put it in housing court or AH?
Another option is to get rid of the kitchen so it isn't an apartment but just additional occupancy space.