water getting in chimney

We have had an ongoing issue with water getting into our chimney during very heavy rain (1-3 inches in just a few hours). Originally we would get 6-8 inches in the cleanout during this rain and the chimney would overflow through the ash doors in the basement and make a mess, and creep into the finished portion of said basement. We just had the chimney cleaned/expected. It was recommended that we cap the chimney, redo the flashing, and get the brick sprayed with ChimneySaver (keeps out water but lets water vapor out). We got the work done and this storm in the North East was the first test. This morning (after 2 inches of rain in 5 hours.... torrential downpour did about half of that in 30 minutes) the chimney still had about an inch of water in it. While it fared much better than before I still don't feel comfortable about saying the problem is solved. So, I have got to think the water is seeping thgrough under grade. The chimney only goes about 12-13 inches under grade and is brick (the land slopes AWAY from the chimney). When we finally get a stretch of dry weather here I'm planning to dig out around the chimney and seal it (and fill in any missing mortar). Any recomendations on what to use? I was thinking roofing tar. I doubt the water is coming UP though the floor of the cleanout, at only 1 foot deep if the water table was that high I think I'd have water pouring through my sump (which currently only has about an inch of water in it and the pump has not yet needed to run). If I seal the outside is there a chance water could still be coming in somewhere else and I could make the problem worse by sealing the water in? I know it must be pourus somewhere because the chimney empties after torrential downpours about an inch an hour or faster. And finally, say I get lazy and want to pay someone to do the work... ABOUT what would the cost be to trench out a 8x2 (approx) chimney about 12-13 inches down, and seal? (in RI). Thanks!!!
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