The US Virgin Islands Police Department (VIPD) said the Southampton resident, 41, was last seen off the coast of St John on March 7.
She was aboard the Siren Song, a catamaran her friends say is owned and operated by her American boyfriend, Ryan Bane.
Mr Bane reportedly refused to allow the police to search his vessel, according to numerous British and US outlets.
A Facebook update from the Find Sarm group on Tuesday expressing hope the media attention "pushes the VIPD to prioritise the investigation".
Ms Heslop's best friend in the UK, 41-year-old Andrew Baldwin, queried the timeline around when the Briton disappeared in a statement on findsarm.com.
He said: "We know that Mr Bane called the local police at 2.30am and was told to call the Coastguard. The Coastguard was reported as saying that it was alerted to her disappearance by Mr Bane at 11.46am on Monday. This timeline just does not make sense to us.
"We also cannot understand why Mr Bane's lawyer has denied officers' requests to search the boat and exercised his constitutional rights to remain silent.
"We know they had dinner in a local restaurant and left at 10pm. What we don't know is what happened in those intervening hours."
The group also published a statement from Ms Heslop's family, who called for assurances that authorities were doing everything possible to locate her.
"We are shocked and distraught that Sarm is missing," they said.
"We would like assurance that the authorities in the Virgin Islands are doing everything possible to find her and that the investigation into our beautiful and cherished daughter's disappearance includes a comprehensive fingertip search of the boat.
"Our daughter is a UK citizen and we ask for all of the support that the UK authorities have to offer. Our thanks go to the local people of St John who continue to search for Sarm.
"We will never give up looking for Sarm and we still have hope of finding her safe."
The VIPD said in a tweet early on Wednesday reissued an appeal for information about Ms Heslop and an 81-year-old man in an unrelated search, adding: "If you have information on either of their whereabouts, you are urged to call police."