Help Fixing Yoda-like Sentence Structure?

I don’t think there is anything wrong with either sentence for each number, honestly. Both pairs are grammatical, although for the second pair the meaning is slightly different because in the first one you are reminiscing about the Angels game, but in the second one it seems to me that you are reminiscing about the signs. The defining relative clause for each one is different. It’s all a matter of what is contained in the defining relative clause.

The second example is perfectly fine. What you are afraid of is ending a sentence/clause with a preposition, for, which is actually not wrong at all. Perhaps, in a very formal context, one would avoid it, e.g. by using for which, or by recasting the sentence, as you did (which changes the meaning slightly in this case).

The first example has a nominal group native speaker English mistakes, where the head is mistakes and the attributes the rest. With such a long string of attributes before the head, I would say it is somewhat less than pretty. But it's serviceable. (Detail: most people would spell it native-speaker in this case, when a two-word phrase is used adjectivally, in order to facilitate the reader.)

Firstly, I'd say that there isn't anything particularly Yoda-like in your examples. Both sentences follow the standard-English [Subject][Verb][Object] ordering rather than a Yoda-like [O][S][V] ordering.

[What][are][the most common native speaker English mistakes]?
[I][was reminiscing about][the Angels game we made the signs for].

However, you are right that there does seem to be a bit of clunkyness in the way you're constructing the noun-phrases for your sentences' objects.

To me, it sounds like you're speaking too quickly and find yourself trapped in a sentence with no way out other than to generate a massive noun-phrase to specify details you had forgotten to include earlier. And, unfortunately, it appears that your reflexes tend to prefer long adjective phrases that inadvertently bury the lede.

For example, lets make your first sentence even more difficult to parse. The object of the sentence is: mistakes in English, made by native English speakers, made most often. How bad can that be to understand?

What are the most common English native speaker made English mistakes?

We're still talking about English mistakes commonly made by English native speakers, but because I've glommed "English-native-speaker-made" together as another nested adjective phrase I'm giving readers/listeners a very difficult job to suss out that "mistakes" is actually the Object they are looking for. Your version isn't remotely so bad as my example, but it still buries your Object behind a mess of adjectives.

The better alternative is to make your object clear early, and then use a prepositional phase to specify those necessary details.

What are the English mistakes most commonly made by native speakers?

Your second sentence could also benefit by breaking out a prepositional phrase rather than making "we made signs for" a direct modifier for game.

I was reminiscing about the Angels game when we made the signs.

Basically, try to break your clumsier sentences into more bite-sized chunks by using a prepositional phrase or two rather than defaulting to chained adjective phrases.

1.

• Mine: What are the most common native speaker English mistakes?
• Correct(?): What are the most common English mistakes for a native speaker?

The first construction seems difficult to understand; there is an ambiguity between the adjective and the noun "English", and even if common sense tells you that it must be the noun, there is still a decision to be made; moreover it is not immediately evident whether the compound is "[native speaker] [English mistakes]" or "[native speaker English] [mistakes] . The second appears to be lacking in elegance.

What I'd write or say

What are the native speaker's most common mistakes in English? (possessive genitive, rather than next (descriptive genitive))

or

What are the most common native speaker's mistakes in English? (descriptive genitive)

or

What are native speaker's English's most common mistakes?

2.

• Mine: I was reminiscing about the Angels game we made the signs for.
• Correct(?): I was reminiscing about the signs we made for the Angels game.

The first construction is correct. Thes second one changes the meaning, and so can't be a correction of the first.

What I'd write or say

I was reminiscing about the Angels game (which)(that)( ) we made the signs for.

or

I was reminiscing about the Angels game for which we made the signs.