Help Shielding RF Anechoic Chamber - FM Stations
Steel? sheet metal?  no wonder 

Also a harmonic of the room resonant frequency could be your FM band and thus amplified.

Anecdotal

When I tested in Paoli PA at a Burroughs EMC test site, we also performed susceptibility tests.  They used a wireless EMI E field sensor to control a 1KW ingress test amplifier on a dodecahedron antenna and the harmonic nulls caused the 1kW RF amp to blast the inside data cables with RF.  They did not know until I pointed it out.  ( circa mid 80's ) So I fixed that.

If you get stuck use a loop antenna to the SA to find near field noise and compare with known good equipment from DELL PC that (hopefully) passes.

Lingren cages are one of the best

The same effect can occur to match the frequency of the cage to multiple wavelengths or outside and poor shielding from the steel.

When I bought a used Lingren EMC cage once used by Stanley, the wireless garage door company it was made with double layer copper screen ( like aluminium mosquito web but pure copper ).  When constructing it every joint was torqued properly and the Beryllium copper fingers were cleaned to seal the gaps in the door. every slot and gap becomes an antenna source of ingress.

So check joints, gaps, slots,  door seal cleanliness, and bolt torque.


  Consider alum screen extra layers over wood. But its only as good as the seals and gaps eliminated with overlap and contact resistance.


You should expect -100 dB minimum from a Lingren design and more likely -120dB.

Look at them and try to duplicate their features.