In theory yes, and if worse comes to worse that is an option.

But its not what any rocket designer would want to do. Having a mechanical system inside of a deep cryo liquid methane is hugely complex and very heavy. Even if you put it outside, you still have deep cryo liquid inside and that would make it even heavier.

Consider that 1kg extra weight on the second stage reduces payload to orbit by 1kg and payload to Mars by much more overall.

How about rotating the rocket so the fuel is pushed outward? The gyroscopic effect could also have a stabilizing effect on the rocket itself.

Is there some kind of material that remains elastic and strong at that temperature that could be used to create a bladder? I assume no, since that seems like something that would have already been done in place of helium pressurant if it were viable. All the rubbery or fabric-like things I know of that are stretchy like that become brittle at those temperatures.

I don't know if such a material exists. The problem is SpaceX operates with Deep Cryo fuel (only company that does so as far as I know). They are literally going to 66K on the LOX and methane.

Helium was just temporary as well so once the actually design system is back with SN15 it should be better already.

The idea that Starship has is to use the fuel and oxidizer in its gas form. So the methane tank contains liquid methane pressurized by gaseous methane.

The benefit of this is that if the engine ingests some of that gaseous methane its less of an issue in terms of engine thrust compared to helium and its possible more recoverable of a situation.

Do you mind if the material is only elastic and strong at that temperature? Suppose that perfluoroheptane is rubbery at those temperatures. (the melting point is -78 °C, which is 195 Kelvin, and SpaceX oxygen is kept at 66 Kelvin)

It works for Mars rover tires too. Want rubbery tires? Use something like perfluoroheptane. Keep the vehicle cold during the trip, or mount the tires in disposable molds that wear away during use.

Not your line of thinking, but I believe ferrofluids were developed to provide control over fuel in zero-g (i.e. a material that is elastic and strong, but that gets mixed with the fuel instead of encasing it)

Doesn't it then get burned? Seems like it would deposit shit in the engine, which is bad especially for a reusable engine.

I believe it's meant to be fully filtered out of the fuel before burning (being magnetic, I think the filtering is a bit easier than some other non-reactive contaminate would be). Most of this is only half-recalled from someone's recent project that showed separating ferrofluid from some liquid on Earth...but I don't recall any other context :/

I've heard of using a gas driven plunger in fuel tanks, but I can't remember the name of the vehicle that did this. Starship uses small "header tanks" that have a similar effect. Weight and reliability are big priorities in this kind of system.

Isn’t helium already used to push fuel into the pumps?

I think it's more to maintain pressure in the tank, in cases where the remaining fuel doesn't vaporize sufficiently on its own (autogenous pressurization). Otherwise, I guess atmospheric pressure or compressive force from the engines/payload could crush the tank. In the case of Starship, the fuel is moved by turbo pumps, which are integrated with the engine, and are powered by burning some of the fuel (there's a diagram of this at https://en.wikipedia.org/wiki/SpaceX_Raptor).

I think that was part of the problem with the last launch. it started to burn some of the helium which caused issues.

I thought they used surface-tension / capillary-action to move the fuel. Like with passive geosatellite heat distribution.

Think a radiator, lots of tiny fins, but all inward pointing in a tube. Coat the fins so they are '-philic' to the liquid. Get creative with the geometries of the fins. Surface tension / capillary-action spread over a lot of the fins in the tube will move the liquid to a sink, like the combustion chamber.