remove inhibitor from monomer
The BHT is only present to prevent small amounts of potential radicals polymerising the monomer. One option is to simply consume it i. e.  Put in one extra per cent of your initiator. 
Otherwise,  similarly to basic alumina, use a basic resin. Once you consume the BHT,  your monomer is prone to polymerisation, so you may need to run it into your reactor under your reaction conditions e.g. flushed with nitrogen, pre-cooled, etc