Is there an easy solution to cleaning the contamination in the fuel supply for Starship?

Speculation alert: A bit of persumption here, as the question probably answers itself. If there was an easy solution, SpaceX would be using it, yes?

Anyway, not knowing any better, let's look at one possibility. First of all, SpaceX's contamination problem results in the icing problem that starves the engines for fuel. It's my guess that this is a large part of the reliability issues that the engine appears to have. Note that I use the word "appear". It isn't an engine problem per se, but a system problem.

The "system" uses the contaminant to maintain pressure in the tanks as they empty during flight. The contaminants come from the burning of the methane and the oxygen in the pre-burners that deliver fuel to the engines at high pressures. So there's some burning of the fuel, and it gets mixed into the tanks. The tanks are holding cryogenic fuels, so the contaminants will freeze and that's where the problems start.

Carbon dioxide is one of the contaminants, and it is the bigger of the two issues. Water ice floats on the liquid oxygen, but dry ice (frozen carbon dioxide) sinks. When it sinks, it can clog up the fuel intakes. No bueno.

The idea I had was to freeze it out of the exhaust BEFORE it gets injected into the oxygen tank. It is mostly oxygen, with the contaminants as mentioned. If the contaminants are frozen out, then there's no more contamination, right? But what to do with these contaminants?

Carbon dioxide (dry ice) can be vented off since when heated, it will revert to a gaseous state. Water ice will melt, but isn't a huge problem anyway if it refreezes.

How to heat it? It may not take much, as the freezing point is about 100 degrees below zero Farenheit. This is actually much warmer than the cryogenic oxygen.

All this may seem simple in concept, but there may be a catch. Or is there? That's what I'm not too sure of. Carbon dioxide will behave differently when under pressure. If you pressurize it, it may get a little tricky to handle.

In practice then, you would cool the exhaust from the pre-burners, using the cryogenic fuel as a means of cooling down to a solid state. Then you would have to obtain a heat source, perhaps from some return gas from another heat exchange in order to return the dry ice to a gaseous state, which can then be vented off.

Easier said than done, perhaps...

Water freezes at a relatively high temperature. Perhaps the water could be used to change the state of the dry ice to a gas.

Could this work? It probably would, but would it be worth it? It all depends on how much hardware you'd need in order to implement it.

There's a lot of heat exchanging going on, and maybe that would make it too complicated.

But this is just a speculation anyway.