How to handle carpet offgassing?

I moved into a new apartment and the carpet is offgassing VOCs. I’m quite sensitive to chemical smells and it irritates my nose and throat constantly. The carpet is around 1 year old, so it will probably take another 3-4 years before the offgassing reduces significantly.

I have already tried the following:

• Asked the apartment office to replace carpet (even offered to pay) with vinyl or something else. They are not agreeing to that.
• Vacuumed and carpet cleaned (Bissell + hot water + cleaning solution) 2-3 times. Didn’t help.
• Tried Pureayre (http://www.pureayre.com/). Didn’t help.
• Airing out with multiple fans – helps somewhat but once the fan is off, the smell comes right back. I can’t run the fan 24×7 due to weather conditions.
• Tried https://www.greenbuildingsupply.com/AFM-SafeChoice-Comprehensive-3-Part-Carpet-Shampoo-and-Sealing-System – Seemed to have reduced the smell from one area but ineffective in another area.
• Covered the carpet with plastic drop cloth and taped the edges with duct tape. Reduced the smell slightly, but not by much.

Short of breaking lease and moving (which would cost me around $6,000), is there anything else I can do?

The carpet is only in the bedroom and the closet. Most of the remaining smell seems to be coming from the closet (40 sq.ft. area), which has a hinged door. Is there anyway to airtight that door?

The closet has no other windows, so can’t ventilate without blowing the closet air into the apartment.