There are two pieces to this problem.
- the geocoder and how well it parses addresses and matches them to the reference data set.
- the reference data
For 1, I have extracted the parser standardizer from PAGC into a postgresql stored procedure (which is OpenSource) and then built a couple of geocoders using that as the heart of the engine.
For 2, and the accuracy that you are looking for, you will likely need high quality commercial data like Navteq or parcel data. Tiger is good for the cost to get you near the location but Title 13 requires Census to fuzzy the address ranges to no single address can be matched to a Census form. So as you found out, Tiger will not do the job.
I have written a lot of geocoders and have one that will work with Navteq and should give you results that are close to your requirements. Check out http://imaptools.com/ and contact me if your interested.