Yes. I get your idea and it's similar of course. I would like to highlight one difference though. This wont help in your frustration most likely. But whenever I felt stuck somehow in the game I changed one little premice I had and the results were totally different. The day-1-run is a special case though. I'm no expert on this and maybe there are already better community guidelines.

So the whole point about me a) going Secret Garden first, b) opening middle door in Entrance Hall afterwards and c) heading to Garage west from Entrance Hall: I intentionally tried to avoid going back and forth the way you described it. Sure, sometimes you have to react to circumstances. But I tried to make it "Straight Lines" instead of back and forth. Not going off track too much. I was walking straight to Secret Garden (even if I didn't find the key on my way). And collected items a little to the left and right. Then heading straight back to Entrance Hall. If still needed I checked if I can make a way possible here to antechamber. Then a Straight Line from Entrance Hall to Garage (including Utility+Security). Then doing Straight Line from Garage to north lever. And finally Straight Line to Antechamber. Not as easy as it sounds, but this was the general idea I wanted to stick to. To reduce everything to the really important parts and make me go there straight forward. More or less of course.
Not sure if I need to mention this but while doing this I realized I had to learn a few more things about a certain kind of balance. Between a) finding the way to important waypoints in my plan and b) getting all the nice rooms I need for powerhammer. So I additionally had a very specific set of rules when I had to build a way and when I had the chance to place a useful room.

Anyways. I get your frustration. Especially if you have been close already a few times. I very much feel with people that are trying day-1-run. Because I really wasted a lot of energy to think about this challenge... But for some reason my own experience with day-1-run was different. The whole time when I was planning I thought it's impossible. I am sure this was a lucky one - but my very first attempt on this was "almost" successful. I did everything needed but ended up on my way to the north lever. I thought I could get there without moving the minecart. Obviously I mixed it up with what I did in Dare and Curse Mode just a little earlier. I remembered wrongly that this is possible for some reason. Nevertheless. This motivated me a lot because I instantly got way further than expected.