No, sorry.
When you forget that passcode, you have only the two options you've already correctly described:
1. Live with the enabled restrictions (restore from backup).
2. Get rid of the enabled restrictions (set your iphone as new).
There should be a 3rd option if you had a less recent backup (made before setting restrictions), restoring from that backup. But keep in mind that restoring operation is "all or nothing"; it means that restore from a backup will overwrite all the existing current data on your device.
Regards
Giulio