I always run synthetic gear oil and never have had a problem. It's not as expensive as an "official" jet pump oil. I also run synthetic gear oil in the chaincase on all my sleds and it works just fine. The oem gear oil for sleds and DOOs looks incredibly similar and feels the same......
My opinion on pumps is I check the oil a bunch. I swap oil a couple times a season because I'm always experimenting but also know that seals can wear, let water in and I'd like to catch it before the pump fails. I do not consider the jet pump a "fill it and forget it" item, I check it regularly.