I'm in the same boat as you with a gallon of DD on my hands. I think using the developer replenished is probably best, with maybe a pretty large working solution, like two liters or so. Replenish 50ml fresh developer per 135-36 equivalent.
Today I'm trying some HP5+ and I'm going to start at 75 degrees F, for 7 minutes, with agitation 5s every 30s. I will season the stock developer with some rolls of film I have lying around, 5 rolls for 10 minutes with the lights on. I'm going to use a 2 liter working solution, and see how it goes. I'm sure the replenished developer will be beautiful.
If you dilute the developer I would use maybe 1+4 like DD-X and discard. Use the same starting times as DD-X, and adjust as needed.