So, basically, what I want to do is prevent useless cluttering by representing each chord as a quarter note, or a full strum pattern.

Is this appropriate?
"My dirt pedals are made of Hulk dick! (and Russian tanks and SRV's urine... which is yellow but full of Blues!)"

supposed to represent a chord strummed in 16ths equalling one quarter note?

I don't think so, if it's played like that it should be written out in full.
What may help with your above example is to split it up into bars (it doesn't look as though it should all be one bar), and make sure the distances between the numbers represent the rhythm as accurately as possible if you haven't done so already.
If it's constant 16th notes (and the rhythm doesn't change), I don't see a problem with it. Write something like "play in 16ths" above it. I would also suggest using bar lines.

There's also an "official" way of notating this that you mostly see in older scores (I guess they used it to save time, space and ink - back then scores were hand made).

If you think it makes your tab easier to read, do it. But sometimes it just makes it more difficult to read. If there's a lot of repetition, I can see it making sense. But whenever you use abbreviations like that, you need to consider if it actually just makes everything more difficult. It may save your own time (then again, just use copy-paste), but do you think it saves other people's time?

When it comes to reading sheet music, I prefer having everything written out. To me it's easier to read 16th notes than quarter notes with slashes.
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