I can see your thinking here - and probably Carroll also saw it! However, If you look at the 'blank' map you will see that it is more probably a comment on one of Carroll's abiding interests - the nature of language. Language (written language) is, of course, 'conventional signs'. The map shows that 'conventional signs' inappropriately used (look at the way Carrol has, for example placed equator anlongside NORTH, has omitted SOUTH completely and has placed 'south pole' in the north). Around this period, actually a little earlier, Carroll began to move away from mathematics into formal logic. Much of Carroll's work centres on the fact that in formal logic the existential validity of the premise is absolute. For example, if the premise is, 'all cats are green', then the conclusion will be that no animal that is not green is not a cat. So Carroll is actually playing with both language and logic here - and very cleverly.
Your second point, I believe, is much nearer to the mark. Very few churches could afford tower bells. One of the main tasks of the verger was to ring a handbell to summon the faithful to church. The verger (Bellman) therefore was fairly univesall a symbol (and metaphor) of the need to respond to the call of the Church.