While this does contain "an answer", it is largely an extended criticism of the question, which contains some observations that just don't make sense.
For example, if the time dilation speed up time on Earth by a factor of 365, trees would grow rings once a day instead of once a year.
This is just wrong. A tree will never grow rings at a rate of once per day; not as a "day" is measured on Earth at any rate. Trees grow rings roughly at a rate of one or so per (Earth) year, period. (That they grow exactly one per year is false; sometimes they might grow more than one, sometimes none.)
Additionally, the time dilation needs to be of the precisely the right "intensity" if it is to provide reconciliation.
This is arguing backwards. If you choose a card randomly from a deck of cards and happen to pick the seven of diamonds, you would not expect some deep, complex set of carefully tuned circumstances that caused that specific result. Yes, you could work backwards to try to determine those circumstances, but arguing that they must have been deliberate makes no sense. It is not a requisite that time dilation is a priori of a particular intensity. Rather, we might attempt to determine what intensity it happened to be based on observed results.
In this sense, asking what the "age of the earth" is ambiguous. It literally depends on who you ask.
No, it doesn't. "Time" as a whole may pass at different rates in different places. "The Earth", however, is by definition its own observer. If I ask "how much time has passed for this specific atom", relativity cannot affect that answer. While it's true that this starts to break down at larger scales, it seems highly unlikely that there would be significant differences in how much time various atoms (a majority of such, anyway) composing the Earth have experienced since "the Earth" existed as a planet.
To make the term precise again, we need to specify a frame of reference. In particular, Young Earth Creationists need to explain why the Bible would use this frame of reference, instead of the Earth's.
Well, here the crux of the problem seems obvious; your hypothesis is that the Bible's timeline is relative to some observation point that is not Earth, and that Earth is "actually" billions of years old.
To the best of my knowledge, exactly no one believes this. The definition of a YEC is approximately someone that rejects the claim that Earth is billions of years (indeed, more than 10,000 years) old. Generally, this belief extends at least to the rest of the solar system.
While the basic premise of the question is reasonable, and an exploration of that premise is beneficial, the details are completely backwards. Time dilation does little if anything to help with the alleged (by Methodological Naturalists, i.e. people who shape their entire world view starting with the unassailable axiom that there is no God) age of the Earth. What it might address is the "starlight problem", i.e. if the Earth is only ~6,000 years old, why do we see stars that seem to be millions or even billions of light-years away? This might be because space expanded at some point and/or because the universe is finite with Earth (or at least the Milky Way) being at or near the mass center. Other answers have offered better references, so I won't bother, except to add that this might also solve the "dark matter" problem.
So... what about the "apparent" age of the Earth itself?
Well... the "irrefutable" evidence that the Earth is really old is Evolutionism. This, however, relies on several logical fallacies and tautologies and is explicitly contradicted by the Bible. It begs the question and is thus unusable as evidence of age. Also, it's irrefutable because it is a logical conclusion of the Naturalist's unassailable axiom that God does not exist. Since this is clearly unscientific, we can exclude Evolutionism from consideration if we are going to consider this matter fairly. (Note that Evolutionism and Natural Selection are not the same thing. NS, which is solidly grounded in observational science, is widely accepted by both Naturalists and YECs. Evolutionism and Uniformitarianism deal with forensic science, which necessarily plays by somewhat different rules.)
The next "most reliable" evidence is radiometric... which actually is not reliable at all; radiometric dating is so heavily steeped in Uniformitarian assumptions (and has been falsified in some instances) that it's a wonder it's given any credence whatsoever. There is certainly no shortage of evidence that much radioactive decay has occurred, and this is widely accepted by YECs, but observing that decay has occurred is not the same as trying to use such evidence to "date" objects. There is evidence that the rate of radioactive decay has not been constant, and has in fact experience a period of great acceleration at some point. For more, see this answer and especially the R.A.T.E. report, volume I and volume II.
The remaining "evidence" (rock strata, fossils, coal/oil, etc.) is explained quite adequately, and in many cases better, by a cataclismic flood (which may have corresponded with the aforementioned acceleration of radioactive decay). I seem to recall reading about such a thing somewhere...
Various observations within our solar system may also suggest that the rest of our solar system is equally young. Again, it depends greatly on whether your interpretation starts with the assumption of great age. When your world view requires that the Earth, sun and planets are extremely old, you will try very hard to find a way to interpret the available evidence to fit that dogma.
For more, I encourage you to poke around AiG, CMI, CRS and/or ICR.
So, as I have hopefully shown, the evidence that needs to be reconciled is not evidence found on Earth, but rather astronomical evidence. And in that respect, yes, time dilation has been suggested as a potential explanation.
However, with respect to this:
The idea that any scientific method of measuring the time of the Earth could be wrong, and a reasonable and logically consistent way to explain it, would be big.
...I'm going to refer you to 2 Thessalonians 11-12:
11 Therefore God sends them a strong delusion, so that they may believe what is false, 12 in order that all may be condemned who did not believe the truth but had pleasure in unrighteousness.
There is, as noted (see also Romans 1:20!), more than enough evidence that Genesis 1 is a true account of history. Those who are willing to accept God have little or no difficulty reconciling observations of the world (i.e. true science) with a literal reading of Genesis 1. Those who are unwilling, who have rejected God and have based their entire world view on that rejection, are under a God-sent "strong delusion". No amount of evidence will convince these people that their world view is wrong. They will go to lengths which to a clear-minded person are inconceivable to rationalize their choice to reject God.
The idea you postulate already exists, and is rabidly denied by Naturalists. Just as they rabidly deny all other evidence that God exists. I don't expect this to change short of the Second Coming.