This is an old thread, but it’s interesting to me since I also wrestled with this. My comment pertains only to 45 degree tossers, which the OP is. Short answer: I am a proponent of the second option he suggested. That is, bringing the tossing arm up the exact same path as for a first serve but releasing it later. This is what it looks to me like professionals who are 45 degree tossers do, and it works.
The alternative he mentioned (moving his tossing arm to the left, i.e., more in front of him) could be made to work if that is more comfortable. There probably are a few pros who have their arms there, but they hit their first serves from there also. That is, they are not really 45 degree tossers. I don’t think I’ve seen any pro start their toss arm at 45 degrees and then move it left in this fashion.
One last thing: sometimes just for fun, on a second serve, I’ll start from a position where my entire body is pointing slightly more to the right than the 45 degree point. In other words, a little more back facing the opponent, so not technically 45 degrees anymore. The toss therefore comes more from the side which promotes the right to left (for a right hander) path that most teachers like to see for a kick serve. It also promotes a better shoulder turn and I get a little more on my racket speed this way. Unfortunately, trying to hit a flat serve from here is uncomfortable for me, so I never do that. I admit that I don’t ever recall seeing a pro vary their starting positions for the first and second serve, so this does violate that.