I'd echo Jason's advice that the OP should reduce the rivets in length, I use wire clippers and a file whilst the rivet is in position
Re rivetting. It's easy to make special r/h rivet snaps for awkward locations. I purchased several packets of loose ball bearings of suitable sizes from the local cycle shop or bearing supplier. A length of steel rod is put in the lathe and a dimple made in the end with a suitable drill. This end is then heated red-hot, the dimple is placed over a ball bearing which rests on a bit of scrap steel and the upper end of the rod is struck smartly with a hammer until a hemi-spherical recess is formed.
The rod is then returned to the lathe for tapering and trimming, plus a bit of filing as necessary.
Mild steel is generally adequate for most jobs, but silver steel can be hardened if a long-lasting snap is required.
This method can be adapted for snaps of any odd shape and size depending what's needed.
For my Simplex, I countersunk the frame holes and hammered the rivet shank into the countersink whilst the head was supported in a snap. A flat file finishes the rivet off flush with the frame. Very easy and quick.