Leon, I'm not clear on your statement about why blown-in insulation may not be possible.
Instead of attacking the points where you feel air infiltrating (as most people do), you need to stop if from exfiltrating i.e. you will have to treat your ceiling as if it were the roof and air-seal that boundry. When this is done, the infiltration will stop. The main problem here is not having access to the whole structure (i.e. the upstairs unit). Dense packing the walls and ceiling with cellulose may be the only practical way. This done, you will probably need to add some ventilation, and if your basement is damp, it must be dried out or you will have humidity problems.
Please give this carefull consideration if you have any combustion appliances. If you were to succeed in sealing every infiltration point, unlikly as that may be, your part of the building would become depressurized (due to the continued exfiltration to the unit above) which could cause backdrafting or spillage of combustion products (eg. CO) in to your unit. You might want to contact a weatherization contractor (not an insulation contractor).