So yeah, both of these things do save time.

Tyrian is a pretty unique game in that it has a common TAS and speed runners tool built right in. You can frame step with one of the cheat codes - Num Lock + Backspace. This is how I tested.

Tyrian looks like it runs at 30 frames per second. On average, being close to the boss saves about 10 frames, and being close to the top of the screen seems to save 8-10 frames.

On top of all of that, Plasma Storm is definitely the fastest way to kill a boss due to piercing and it's rather unique instant deploy. I'd thought the game skipped ahead, but with some further testing it turns out that you can literally deploy all of the plasma on single frames, so it looks like 6 frames in total. The game doesn't appear to know how to handle that with the pause cheat so it just acts as if they were all deployed on the first frame.

You should also be able to get a quick kill on the first boss (AKA, kill it without leaving the top part of the boss behind to finish off) if you wait for it's firing noise every time. Whether this actually saves a huge amount of time is doubtful though, as, I'm guessing the boss is vulnerable shortly before that. It might actually be faster to just use the close range and top screen warp time saves and not really care about this.

If executed well, you might save about a minute over the course of the 30 levels with bosses where this is applicable, but obviously some level layouts might make this unsafe to do.

Here's the video:

I also test out how many frames it takes for the SDF to fire of the screen and recharge, and for the Plamsa to be off the screen. And in case you were wondering how many frames it takes to get full shields, and out of invulnerability, that's in there as well. Spoilers, it's about 100 and 200 frames respectively.

Just some thoughts based on observations:

1. The closer you are to the top of the screen, it appears like it takes less time to clear the the level after beating the boss. You seem to see the text faster.

2. This is fairly logical, but weapons that are fixed and do piercing damage per tick (like the SDF Cannon, Plasma Storm, and other side kicks and specials) appear to do their damage quicker when you're closer to the top of the screen.

I'll report back if I prove these.