Looking at unfinished bits: do you really feel the need to spell out the advancement like that? I thought increasing damage, etc, is something DMs are supposed to figure out themselves? That said, I'm ok with increasing the number of pseudopods to 15 and 20 for G and C and just stepping up the damage one step per size category.
There's nothing in the Monster Advancement rules about increasing the damage of special attacks, it only allows for increasing the damage of weapon attacks due to increased size or Strength. There's nothing about the DM increasing the damage themselves.
There are plenty of examples of advanced creatures published by WotC and Paizo whose special attacks still have the basic range and damage - e.g. the Maurid Advanced Chimera in
Dungeon #112 has max Hit Dice for a Chimera (27 HD), making it Huge size, but its breath weapon is still a 20-ft. cone doing 3d8 damage like a standard 9 HD Chimera. It doesn't even do 4d8 damage for being a size larger, since it's not a natural weapon.
To make a monster's special attack damage increase with advancement it really needs to say so in their description, otherwise under RAW it'll do the same damage as a non-advanced creature.
I'd set the beamtorches' damage so they pretty much match the melee tool's damage, since the original monster did the same damage no matter the form of the pseudopod-tip it hit an opponent with.
A Gargantuan Silver Slime Megalium would do 2d6+11 plus 3d6 energy (or 2d8 energy if we have the energy damage size-scale as if it were a Fire Elemental), which suggests we should have its beamtorches do about 6d8 damage.
A Colossal Silver Slime Megalium would do 3d6+15 plus 4d6 energy (or 3d8 energy if we have the energy damage size-scale as if it were a Fire Elemental), which suggests 8d8 or 9d8 damage for the beamtorches.
The above does not allow for ability score increases from its Hit Dice increases, which it'll likely apply to Strength or Constitution.
