I have never heard of an alloy cored push rod, Utterly pointless, the tubular variety will be as stiff, and lighter. But there are many spivs, profiteers and wasters who have nothing better to do than push ali upon unsuspecting customers, when it is often, but not always, one of the most inappropriate materials for the job. Anyone for an alloy crankshaft? Rods? 100000 mile warranty on them? 100 miles warranty? 1 mile warranty? (Enough for one drag race, maybe.) And the stiffness of a rod or tube is concentrated towards the outside, so drilling a hole down the middle makes hardly any difference. If I remember correctly, the stiffness is proportional to R4-r4 while the weight and tensile strength are proportional to R2-r2 where R is the outer radius and r is the inner radius. Compressive (buckling) strength gets a bit more complicated, but the straightness, related to quality of manufacture, helps. Ever looked at the diameter of the anti-roll bar drop links on a Mk 1 Ford Focus, which, as it is a very heavy bar, carry rather large peak compressive loads during hard cornering? Careful manufacture and the correct choice of material mean a lot.
I don't think that the Mini pushrod tunnels are large enough to take them, but in general the best material for pushrods would be tubular carbon fibre. But if you (a hypothetical "you", not any person on this forum) are obsessed about valve train mass to that degree you really need an overhead cam, and you do away with the pushrod tunnels to get more space for inlet and exhaust ports, then you realise that the layout is still restricting breathing, so it has to be crossflow, and then you will be wanting 4 vales per cylinder, so go down to the scrappy and find an entirely different modern engine.
All very well, but I have seriously over-revved several Mini engines, admittedly all 998 where the safe rev limit is higher than most other sizes, and nothing broke, certainly not the standard pushrods or pressed steel rockers. But I did keep my valve springs in good order, always replacing them at every major engine overhaul, which helps to avoid valve bounce, the cause of premature death of various valve train components.