You've mentioned LP relay... . have you tried a NEW relay? They do go bad. Remove the relay & break it open to note corrosion on the contact surfaces. Also, I had an intermittent problem w/my LP and after much head scratchin' found the pin connector at the cowl had worked loose. (attached under the cowl just above the fuel filter) Seems the white connector lock had unlocked allowing the connector to work loose.
Also a loose injector line could prevent sufficient pressure to "crack open" the injector causing a rough idle/run. Are you noticing any leaking at the injector lines?