What is your recommended way of managing a locally advanced bulky base of tongue (BOT) p16 negative squamous cell carcinoma extending into multiple structures of the supraglottic larynx?   

ChemoRT. We did pretty well with RT prior to HPV. Surgery is likely no better and more morbid. 

The only randomized study that I am aware of that compares upfront surgery followed by adjuvant RT with chemoRT for locally advanced squamous cell of the head and neck is the study by Iyer et al., PMID 25639864, and it showed comparable results in non-oral cavity or maxillary sinus sites, regardless...

Resection with free flap reconstruction performed by a surgeon experienced in microvascular surgery, preferably at a tertiary hospital, followed with RT or chemo-RT based on pathology.