I didn't misuse words. How can you accuse me of misusing something you started with an incorrect definition of?
Easy- you tried to use a late-plot plot device as a perjorative for backstory. It was a misuse of the deus ex machina.
Yes, and here the path to Andromeda would be deliberately crafted just to get us there. It doesn't have to be realistic from our universe, but has to be realistic in the Mass Effect universe. A wormhole suddenly appearing would be artificial. We can roll with it because it's sci-fi and those things happen in space stories, but it's still a cheap way out when you've already established cool ways for your ships to get around. That's why I like the Conduit idea, though that probably needs more work than I laid out. Much like plot holes, it's not that whether or not something is contrived that is subjective as much as it is that how much it bothers you is subjective.
Unlike contrivances or 'meaningful' experiences, plot holes are objective. A plot hole is a logical incosenstency- not to be confused with 'doesn't make sense to me'- or an impossibility in the plot. They can be objectively identified and disected.
It's frequently abused for 'things I don't like,' much like deus ex machina, but eh.
Interestingly, and playing into the problem of subjectivity you raise, part of the problem is caused by the title and the fact that it is known that we are going to Andromeda. This leaves us here wondering how this is possible. Had they simply started with the journey, even something like a wormhole suddenly appearing wouldn't have seemed as odd because it would seem like a natural event that took us to Andromeda rather than a solution to the problem of a predetermined setting change.
If this is a problem, it sounds rather self-inflicted. If a sudden introduction of a wormhole for the purpose of intergalactic travel wouldn't strike you as just as odd or contrived, then there's really no basis for any writer to particularly worry.
Hawke's travel isn't comparable in the least. Boats exist in the Dragon Age universe and they were traveling across the sea to another area of Thedas that we already know about and people from Ferelden travel to, or vice versa, regularly. Adding to the list of terms your don't understand, this is not a handwave. It's merely Varric telling us about it rather than us following Hawke do it. It fits entirely within what is known about the universe and does not require anything new or unknown. This is like if you were watching a movie and a character says they were going somewhere, then the film showed a map with an airplane moving and drawing a line to show the path, then the next scene showed them in the destination city. There is no plothole or hand wave, but merely a different, quicker way of showing that the trip happened. Ironically, your comment that the answer to Andromeda is just "technology" is the definition of a hand wave.
I'm amused you consider tvtropes laconic entry an authoritative definition- while ignoring the less laconic, but more relevant, definition of the same site's same article's main page.
A Hand Wave (also memetically called "Scotch Tape") is any explanation involving the backstory, a retcon, or a use of phlebotinum, which is noteworthy for its lack of detail or coherence.
Which would apply to Hawke's escape from Ferelden, as told by Varric. It is backstory, it utilizes a variation of phlebotinum (in this case, the plot device that is Flemeth), and it's remarkably lacking in detail. Handwave, as used by TVTropes.
I'm not inventing the problem. The problem was created by the title, setting, and premise of the new game.
Dudette, you just admitted that you wouldn't find a suddenly introduced wormhole contrived so long as you didn't know about it ahead of time. And you didn't so much as blush in suggesting that magical trees could dominate Andromedea so that milky way immigrants won't be hopelessly out-settled and out-teched as any milky-way equivalent species would have done.
The problem is pretty much on your end.
Why Reapers didn't go to Andromeda is only an issue if it were possible for them to do so, which only matters if "Reaper tech" is the answer to getting to Andromeda.
You probably want to back up a sec, because getting to Andromedea isn't the technological challenge. We could send something to Andromedea- it might take us way more time than we wanted, but Newton's Third Law makes crossing galaxies... well, the crossing's easy.
The Reaper tech angle is about getting to Andromedea quickly. As in, quickly enough for us to care and find plausible. The technological limitation Iakus is fond of point to is drive charge buildup from going FTL with a mass effect engine. Don't use mass effect FTL, and you won't get that limitation. It'll take longer- a lot longer- to go 2.5 million lightyears, but the Reapers have time. They've had, on the conservative end, a billion years.
As for why there isn't an all powerful Prothean-like empire ruling Andromeda, if there isn't, all you need are things we had in the Milky Way; either the most powerful race is like the Asari and focuses on collaboration and cooperation rather than domination or a galactic Tuchanka where everyone is constantly fighting and destroying for them to advance very much. There are other ways to do deal with that as well. Maybe a race like Tolkien's Ents that are so long lived that they do everything slowly and thus don't progress quickly. That would make an interesting contrast against short lived, get things done races like the Salarians and Humans.
So... contrivance. And/or space magic, to make humans more special in two galaxies in being so quick and adaptive and innovative.