Actually, a cartridge spacer, if flat across the entire surface, will make the problem worse. The SME arm has this problem with tall cartridges or thick headshells. In order to open up space between the cue pad and the tonearm, you need to add a shim forward of the cartridge bolts and tip the cartridge down in front. Then lower the tonearm at the tower until the cartridge is level or obtains whatever VTA you were using.
An Arche headshell enables this adjustment without a shim. Unfortunately it's expensive.