Hmm, well if there is enough space to safely use it and you just need to remove the dust cover it should be fine, but I have done this with mine for rumble feedback etc.. as you say, use sound damping sheets everywhere possible, on the bottom of the table and on all the inside areas of the cabinet this will reduce a lot of the feedback trapped in the cavity, and also eliminate echo.. you can go on partsexpress.com and get the pretty heavy thick black rolls that are like 3 foot X 3 foot plus size pieces and cut exact sized panels of Black to look nice in the cabinet..
They are pretty cheap too at like 10 to 15 bucks for pretty large rolls. I did this on my dustcover and it really reduced a lot of noise and made soundstage better, so whatever your dustcover is trapping now is gonna be very similar the cabinet around it will, but at least its hardwood not plastic. I have also deadend the tonearm with excellent results, but this will require the right type compound lightweight etc.. for this,, Marigo dots I believe is one that is used to good results, they have those at musicdirect.com I believe.
They are pretty cheap too at like 10 to 15 bucks for pretty large rolls. I did this on my dustcover and it really reduced a lot of noise and made soundstage better, so whatever your dustcover is trapping now is gonna be very similar the cabinet around it will, but at least its hardwood not plastic. I have also deadend the tonearm with excellent results, but this will require the right type compound lightweight etc.. for this,, Marigo dots I believe is one that is used to good results, they have those at musicdirect.com I believe.