I asked for a quote to use my companion ticket and was given only 1 flight option. I do remember when "thankyoucompanion.com" was alive, multiple "lowest fare" options were available. Is it same now? Should I ask a concierge for more flight options?
If you have another option that you think has the lowest fare, supply that to the concierge and see if they're able to find it on their end. My experience on this has been 50/50, but it does work from time to time. It might also depend on the agent you're working with. Good luck.