Brian...Stack three or four and cut a bunch.
I bet ... two or four will turn out great.
If you only want to cut one... I don't understand ... Either way, use a small blade.
Also, blades cut on the down stroke ... so it's the bottom you might have a problem with.
So..... when you stack cut, usually it's the bottom one that takes the abuse.
A picture of pattern#1340 Songbirds would be nice... could help better.