Steve, I'm glad so many people here have added some helpful tips - as I said, you'll find everyone on here will be very helpful, as I've had good cause to find out myself.
Gilljc raises some interesting & valuable points (e.g. I worked with a Dremel that only took pinned blades for a long time, and was able to do some fairly intricate inside cuts).
Though I'm not familiar with the Steve Good rabbits pattern you mention, are you sure there isn't another way of attacking that curved paws problem with your existing pinned blades? For example you can cut part of the curved paws, then continue the saw cut out into the waste wood as the curve tightens up. Leave yourself enough room in the waste to be able to turn back round, then cut back into the curve from a slightly different angle, repeating several timesif necessary, as dictated by the curve on the pattern versus the tightest radius your blade will cut. And you'll probably have to finish off by going all round the paws again to cut off the little nibs that you've left behind.
Yes, that's time-consuming compared with cutting out with pinless blades, and will waste a bit more wood than when cutting with pinless blades too, but until you can fix up pinless adapters or change your machine, just as gilljc says, you'll be surprised what can be done with pinned blades after a bit of practice.
HTH, good luck.
AES