Saving large black olive trees

I just purchased a house that has been vacant a while in Miami, Florida (zone 10).
The house has been neglected and need some repair and updating, all along I was not paying too much attention to the trees because many of them were damaged by hurricane Wilma and a lot of clean up needed to be done to even see what I am dealing with.
There was one young oak tree that basically toppled so I had it removed and grinded the stump.
There was a mango tree with a large vertical split in the main trunk which the tree guy told me had to be removed and grinded.
Two large mature (over 40' tall) black olive trees on the property that had a lot of broken limbs and dangling debris that needed to be cleaned up and trimmed clean.
However, the most problems are three large black olive trees on the other side of the sidewalk (so it's not in the property) but I am responsible to maintain but's it's the city's property and they are protected species.
I thought the tree guy would recommend trimming them but he recommend I remove all three of them...and ask the city for permission. His reason is that they had damages when Wilma came through but they were not treated and dealt with in time, so now he sees rot and termites and unbalanced growth. Now I don't want to cut down three large mature trees even if the city gives me permission, they are really nice trees...
I don't know whether the termites have penetrated deep...he kicked the bark near ground level and saw some rot but does it mean the entire tree is infested?
Out of the three I do see one that is badly unbalanced and leaning to the street where the root on the other side is forced up and pushed the concrete sidewalk up, he says this is a hurricane hazard waiting to happen.
I am torn as to what I should do. I called the city and they said they will send someone out to see if they need removal in a few MONTHS because of hurricane backlog. I don't really want to remove them. Any advise what I should do?
Thanks in advance,
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