To move along is a collocation that means 'to stop loitering' or 'to stop gawking at something'. A policeman may say to the loiterer(s) | gawker(s), "Move along!". However, adding a prepositional phrase, e.g. "to move along the street", makes it no longer a collocation, and then it does express the idea "to proceed down the street".
People also say, "I've got to move along", which means, "I must be going", i.e. "It's time I left". This meaning is very close to the policeman's "Move along!"
To work along does mean 'to continue working, to keep at one's task'
The lights went out, but they lit candles and worked along.
Along this Way: The Autobiography of James Weldon Johnson gives another example.
Note: 'to work along with someone' means 'to cooperate'.
To 'go along' is a collocation that means 'to acquiesce'.
See if you can get him to go along. If he doesn't play ball, threaten to cut his funding.
'To pull someone along' means to proceed, with another person more-or-less "in tow", as in your example.
'To walk along' can mean 'to stop loitering', like 'move along'. It can also mean 'to proceed'. An example of the latter can be found in The semantic development of words for "walk, run" in the Germanic languages Roscoe Myrl Ihrig (Chicago, 1916).