If you look at the CFR's you can actually get an apprentice steersman endorsement with a 100 ton mates license. In other words, you don't need the 200 ton mate. The 100 ton is the lowest level license for the steersman.
After going through the steers man and 200 ton mate courses and sea time requirements I would recommend just going straight for a 500 ton mate and getting the TOAR signed off. You don't even have to mess with the steersman for 360 days. The other catch with the steersman is if you're sailing as a deckhand while you have your TOAR signed off make sure your company will list you as apprentice mate steersman on your sea service letter. The NMC will not give you the 360 days if you're sea service letter says you're AB.