Sympathise Marcus, been there (broken ribs and cartilage tears) heaps - in fact quick check in the old brain box would be over ten times with at least two of these during periods when I've been paddling regularly. With that behind me have to go with your savvy doctor 100% - "there is no treatment but time and 'if it hurts, don't do it'." (Well, do it a bit less was my approach.)
With busted ribs there's a period where paddling is clearly not possible. After that point however, even when with some adjustment in the boat you can kinda-sorta paddle ok, things like lifting a ski or a 22kg plastic onto and off a vehicle or - gasp - getting back into a boat when you've come out, are extremely difficult. (Try scuba diving too early - ooo that didn't end well.)
The cartilage injury is a dicky one because unlike a knitting bone which seems to have some degree of its own integrity (after a point), I reckon you can re-injure or exacerbate the cartilage problem if you do too much. Regardless however that's where your Doc's advice is good, something that most blokes just end up doing anyway, stick a band-aid on it and get back to work until the bleeding gets in the way again haha.
Though festina lente a good adage - making haste slowly - I sympathise with trying to push the envelope. When this becomes counter-productive and you're no longer healing effectively, that's when you just have to step back a bit and let nature do its work. To my knowledge there is no physio or exercises that make a difference however that worthy of your own research. For cartilage healing and general joint well-being especially in the long term (I suggest you take this stuff forever and ever) I'm a big fan of glucosamine (with chrondoiton). Again read up on this, but has worked for accident prone me with two meniscal tears (knees), three shoulder ops, rib cartilage, plus dislocations of various joints blah blah blah . Bloody marvel of modern medicine but everything still well-oiled and working. Only get a stiff back from sitting on my arse for too long..
Good luck, all will be fine in time.