Just some thoughts. (again no real experience, I've been very lucky and not had enough IVs to warrant one but am a good purveyor of medical science so that's my point of view)
-Could you take an oral anticoagulant each day (coumandin comes to mind), you'd have to be monitored to make sure it's not more than a therapautic dose. It seems from my reading that a low molecular weight heparin following placement of a port and then therapautic doses of oral anti-coagulants have been shown to reduce clotting in cancer patients who receive ports. Several medline articles out there that your dr. should be able to look up. But if you are using ibuprofen therapy this option might not be an option b/c coumadin and NSAIDS interact. I would probably also not go this route if you have hemoptysis (your dr. would know more).
-Some research suggests placement may have to do with clotting, as it seems your doctor suggested, right side insertion with ultrasonographic technique at the junction of the superior caval vein and the right atrium has the lowest risk of causing clots. First 6 weeks after placement are the time when you will potentially have the most problems with clotting b/c after that the 'foreign invader' attack on your port decreases.
Sorry I can't help more. Just not seeing a lot out there... I think your need is not necessarily a new port but appropriate post-placement care and anticoagulation. I'd get a second opinion or a third after the recommendation with a specialist. By fax if you have to if you aren't close to a major medical center with someone specializing in factor 5 and port placement. You might try an oncology center since they tend to place more ports than anyone. Best of luck!