You're assuming guilt. Unless you have some special knowledge of this particular individual, the general ideal we originally strived for in the US Justice system is a belief that individuals are considered innocent until proven guilty. It's fine if you want to believe that yourself, but it's contradictory to how the US justice system is supposed to work.
I'm of the opinion that trials should be system where both sides should be allowed to put as much money as they want into a trial, but that they need to put that money into a pot that is divided equally between the defense and prosecution. You cannot have justice when there is financial asymmetry.
This would allow trials to be as cheap or as expensive as necessary to determine the truth. It provides a great disincentive for either side to pour money into the process if they know they are in the wrong going into a trial.
Stipulate that some significant portion of the accused are, in fact, guilty. We don't know which ones, but we know in the abstract that they exist. We also know that the overwhelming majority --- not all, but most --- of the guilty accused know they're guilty.
In your proposed system, what's the incentive that prevents the guilty accused from allocating infinite resources to their case? Why not do that? These are people who've drawn off-suit seven deuce in the poker game of justice. What would they have to lose?
Let them have their day, even 10 days in court. If they're guilty it will still stick. If not they should walk, no matter how long it takes to get to that point.
The way to deal with the overload is a many pronged problem, for one you could decide not to have so many crimes on the books, second you could decide which crimes are to be dealt with using fines and which are to be dealt with using prison time, and prison time could be seen as a measure of correction rather than one of punishment or revenge.
That would mean that there would be a lot less prisoners and that in turn would upset a whole pile of applecarts but on the whole that's not a bad system to have.
At least you won't have 1% of the population (and 2% of the adult population) behind bars which is generally considered to be a good thing because it takes people out of circulation causing a domino effect into the next generation. Kids of convicts are more likely to become convicts themselves.
Compromising the right to a fair trial on cost basis because you're scared the 'guilty accused' will hog the system has a much higher cost in the longer term.
How is the very concept of an appeals system not abhorrent to you? It's based on the idea that the accused receives a finite number of opportunities to vindicate themselves, and that number has an arbitrary cut-off.
An arbitrary cut-off is indeed a strange thing to have, probably some element of practicality went into designing it. Where I live there are a number of courts where one can appeal, I personally think that the ideal would be a court where no conviction would ever be overturned should be the cut-off. We're definitely not there and that system isn't perfect (nor will it likely every be), but it is one of the reason why I am mordicus against the death penalty.
Too many cases got overturned many many years later and in plenty of those cases the accused had already been executed. See also: project innocence.
Justice systems will always be imperfect but regardless of that we should strive to improve them and find better ways to release those that are innocent as fast as possible (and, incidentally, to make them whole).
The state and its functionaries should definitely not be rewarded on metrics that might disadvantage the innocent.
