Endlessly pestered stranger with a higher asking price (7)

I believe the answer is:

steeper

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'endlessly pestered stranger with a higher asking price' is the definition.
I can't judge whether this defines the answer.

'endlessly pestered stranger' is the wordplay.
'endlessly' means to remove the last letter.
'stranger' indicates an anagram.
'pestered' with its final letter taken away is 'pestere'.
'pestere' anagrammed gives 'STEEPER'.

Can you help me to learn more?

(Other definitions for steeper that I've seen before include "More inclined" , "greater inclination" , "More precipitous" .)

I've seen this clue in the Sydney Morning Herald.

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