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Roobarb,
Try searching "Lloyd's List" available from the British Newspaper Archive. Use the search term Quebec.
I doubt it will give information on the said desertion but it will narrow down the names of the ships which were in Quebec. You can then search the relevent Crew Agreements at TNA.
The Crew Agreement of the last ship you know he was on in 1856.  Doesn't it tell you the name of his previous ship?
Do you know his Seamans Ticket number?

SW

"at Sunderland" makes a lot more sense than my Sundius theory.

The "William Penn" that was loading in London was on the London-New York run, so I am now wondering if there was another vessel of that name operating out of Sunderland.

There were two vessels with the name WILLIAM PENN operating in 1867. The ship you refer to was a steamship registered in Waterford official number 49738. The other registered in Sunderland, a sailing coaster O/N 1815 owned by W S Pallister. In my opinion this is the possible vessel in contention. 
She put in to Portsmouth with a broken bowsprit, jib boom etc on 2 Jan 1867 voyage Sunderland for Cowes. The weather was gale force winds and snow storms.This would have made for a very uncomfortable voyage and maybe the last straw for young Henry.
For what it's worth I think Lund is a miss spelling of the abbreviation, Lond. (London) Maybe she also put into the Port of London.
.The 1867 Crew Agreements and logbooks of this vessel are in the Maritime History Archive.
https://mha.mun.ca/mha/holdings/viewcombinedcrews.php?Official_No=1815
This should prove wether or not Henry was on board.
However we should not discount the Steamer WILLIAM PENN Her Crew Agreements maybe on line from "Ancestry" If they have a subscription, it may pay the O/P to look there first.

SW
 

I'm now uncertain if this was the older Alexander McKellar (shown above?) who is in the war grave -need to try to get ship's log, if possible.

 FindMyPast should have basic details of how he met his demise. Taken from the Deaths at Sea register.
https://search.findmypast.co.uk/search-world-records/british-armed-forces-and-overseas-deaths-and-burials
There were nine British and Empire ships around in 1917 with the name KING EDWARD. So if you do visit Kew you need to find the correct one.
I suspect it was the Glasgow registered KING EDWARD official number 113963 but I could be wrong.
https://www.crewlist.org.uk/data/viewimages?year=1915&name=KING+EDWARD&steamsail=Steam&year=1917+&submit=enter
The DAS register should tell you the official number of the ship he died on.
The ships Logbook should tell you in detail the cause of his demise. The ships Crew Agreement should tell you personal details, such as his last address, NOK etc. Which should prove wether or not it is the person you seek.
Search TNA catalogue via Official number.
https://discovery.nationalarchives.gov.uk/results/r?name=Search&_cr1=BT%2099/3328&_aq=113963

SW

On British ships, Greaser would have been classed as semi skilled. His primary function would involve oiling and greasing the ships machinery.  He would also undertake other engine room duties such as cleaning. Known as a Wiper on US vessels.
Other records.
If he had further MN service after 1921, then details should be on FindMyPast. Assuming of course they have not been lost or destroyed.
You say he deserted from the Army in 1915/16.
I would take a look at the crew agreement of EMPRESS OF FRANCE  official number 136266, covering the date 11.3.1921 to see if he had a previous ship. Available from the British National Archive. You would need to visit or appoint a researcher to look for you or ask for a quote for copying from TNA.
https://discovery.nationalarchives.gov.uk/details/r/C2480954
If you do get hold of his previous ship, if any. Then come back to us and we can tell you how to proceed futher. Merchant Navy Personal records for the period of the First World War have been destroyed so the only way is via Crew Agreements.
Cannot find a WW1 medal listing for him.
https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/merchant-seamens-campaign-medal-records-1914-1918/

SW