Brent & Others; Ordinary hacksaw blades are indeed far too wide. Go to a hobby store (you where they sell stuff for the mini build folks - doll houses & mini furniture comes to mind). They should have very thin saw blades supported in a reinforcement bar and fitted with a handle. Dug 2 of mine out and the blades are 4.5" long, one has 32 teeth per inch and the other has 42 both are .010 thick.
I use the 60 deg. just too slightly deepen the spacer scribe lines and give more of a guide for the saw blade and then again to take off any sharp edges on the diamonds. By a light touch - I mean light. Should I want more than absolute flat I go a little deeper with the 60.
You will also find these little saws good for straightening out lines / laying out straight lines. If anyone needs, I could take a pic. and you could post it here, would need an email addy. --- John