I'm not familiar with flight options to Anegada.

You can get from Anegada to St John fairly conveniently and inexpensively via ferry & taxi on M,W,F,Su. Ferry departs 0830 from Anegada to Roadtown. Figure you are there latest by 1000, then taxi to West End. Have waterfront lunch at the Fish n' Lime Restaurant then stroll over for the 1215 Inter-Island Ferry to Cruz Bay. Should be thru customs & immigration by 1300. Total ticket & taxi cost about $100 pp + $20 departure tax per person. Walk over to The Landings for a well-deserved Bushwacker.