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Guernsey records are at the Priaulx Library in St Peter Port.

Many army pensioners made their homes in Jersey in the first half of the 19th century. The main reason was usually financial, the cost of living here was considerably less than on the U.K.mainland.
There was a constant military presence on the island from the late 1700s because of the threat from the French - Francis may even have been stationed here at some point.

Bridget O'Neill, wife of Frs Welsh died at No 4, The Parade in St Helier on 4 Oct 1858, aged 60

The death of a Philip Heaney is recorded in the index for St Helier cpvering the period from Oct 1979 to April 1981. It is Volume 80 and is on page 75 which would make it towards the end of that time frame.
Jersey Archive has a copy of the will of a Philip Heaney of Mont Plaisir Guest House, Midvale Rd, St Helier and formerly of Overdale Hospital. Probate was granted in Jan 1981.

No guarantee that this is your grandfather but you can get a copy of the will from the Archive. You could try messaging the Registry Office,sir@gov.je, for details from the certificate - make sure you give them the details of the index or they will charge you a search fee.

As you say St Martin was 'home' parish to many Noel families and my take on it would be that the clergyman added 'of the West' to indicate which part of the parish of St Martin Clement came from and thus differentiate him from other Noel families.