When two verbs depend on each other their tenses must have a definite relation to each other. "I shall have much pleasure in accepting your kind invitation" is wrong, unless you really mean that just now you decline though by-and-by you intend to accept? or unless you mean that you do accept now, though you have no pleasure in doing so, but look forward to be more pleased by-and-by. In fact the sequence of the compound tenses puzzle experienced writers. The best plan is to go back in thought to the time in question and use the tense you would then naturally use. Now in the sentence "I should have liked to have gone to see the circus" the way to find out the proper sequence is to ask yourself the question— what is it I "should have liked" to do? and the plain answer is "to go to see the circus." I cannot answer—"To have gone to see the circus" for that would imply that at a certain moment I would have liked to be in the position of having gone to the circus. But I do not mean this? I mean that at the moment at which I am speaking I wish I had gone to see the circus. The verbal phrase I should have liked carries me back to the time when there was a chance of seeing the circus and once back at the time, the going to the circus is a thing of the present. This whole explanation resolves itself into the simple question,—what should I have liked at that time, and the answer is"to go to see the circus," therefore this is the proper sequence, and the expression should be "I should have liked to go to see the circus."
If we wish to speak of something relating to a time prior to that indicated in the past tense we must use the perfect tense of the infinitive? as, "He appeared to have seen better days." We should say "I expected to meet him," not "I expected to have met him." "We intended to visit you," not "to have visited you." "I hoped they would arrive," not "I hoped they would have arrived." "I thought I should catch the bird," not "I thought I should have caught the bird." "I had intended to go to the meeting," not "I had intended to have gone to the meeting."