I agree as well, wait it out. I believe everyone should pay their dues no matter what profession they choose but in our case especially becoming a professional pilot. And that doesn't mean just getting your tickets. You should sweat it out a little while in a small single engine plane doing CFIing or approaches down to mins, while building your multi on the side or in your case MEIing. I personally skipped the whole CFIing thing and built over 1000 hours flying skydivers. I had an absolute blast doing it, plus when the day was over I was basically paid out in beer and drank the night away with the other pilots, skydivers and the boss while sharing the stories of that day. I can honestly say that I hand flew all my hours up to the point where I got hired on to the airlines, where I was around 1400tt or so. To this day, I still hand fly the jet up to 18k on my legs and sometimes below 10k depending on workload, it makes it more fun plus I miss the piloting feel. AP is just a tool and you can tend to forget that after a while.
Beyond all that, right now your experience level is really not very high and it may make it more difficult for you throughout sim training and especially going through your first hundred or so hours after IOE. IOE captains are there to train you, that is what they get paid for. Regular line captains expect you to know what you are doing and don't want to baby sit you. Dont get me wrong they will help you but after several mistakes, especially the same ones over and over again, the captain (at their will) may write you up and then you have to deal with retraining and a possible carpet dance with the Chief Pilot or the Feds blah blah blah...
Moral of the story is get experience however you want and have fun doing it! You will be much more respected on the line and feel much more ready when "your time" comes. Good luck to you!