To me, spacer springs / packing seems the only viable option.
Many people install spacers in used JDM cars for improving ground clearance, but car handling, suspension, etc. can become compromised after installing them.
Well it seems strange to me that previously, you were using 195/65/15 with wheel cups (the tire and rim size is 15"). Then you installed 15" alloy rims, and the problem started. If I am not wrong, if tire and rim size is the same i.e. 15" (irrespective alloy rim or steel rim), issue Hona nai chaheye. The problem may also be somewhere else.