I understand what the homogonized string is in the points, but am not sure what the parcel strings look like if they are homogonized strings in two fields. You have only written a single string as the range and not two separate strings, so that makes no sense to me.
The addresses need to be standardized, since 1st avenue and 1st ave won't join without some further processing to a standard format, either using geocoding tools or python scripting/replace calculations.
If the street names were identical and only the numbers were the issue a python script using cursors and dictionaries would not be that hard to write to split the strings, match the street names, and evaluate the ranges to write a common single numeric field to both feature classes with values representing each range. But before providing an example script I would want to know exactly how the strings are formatted and how much standardization needs to take place to get the street names to match exactly. Python cold also employ a SoundEx algorithm, but more false matches would occur the farther away you get from exact matches.
Since you are dealing with both sources being spatial data, a Spatial Join with buffering could play a role in reducing the possible range candidates and help with the street and range matching process. A screen shot of the point and parcel distribution would be required to evaluate whether or not that is another possible approach.