I'm an old cardiac surgical RN, and IF you do not have any renal (kidney) insufficiency and your not a heavy alcohol user then you are going to be better off taking the tylenol in the dosage you stated than having pain that will limit you from activity. Tylenol does not affect clotting as a general rule.
Long term use to ME, does not mean during post operative healing. Long term to me would be daily...for months or years. So you should be fine. Tylenol works different than the NSAIDS of which Alieve and Motrin as well as Aspirn are examples. NSAIDS DO affect clotting.
As long as you get enough fluid then all is well. You are not taking maximum dosages if your only taking 2 500mg tablets twice a day.
However, IF you take Vicodin or Percocet (a narcotic with tylenol or acetaminophen) then you need to make sure that you are not taking those pain pills at the same time you take the tylenol.
Your cardiac doctors office will have a registered nurse that you can call and talk to. You don't have to talk to the doctor. I know many folks don't like to call and "bother" the doctor with little questions. That is what the nurses job is, to answer questions and teach.