As for my knowledge and experience of it HP is what Stoneskins HP is affected by. So maximizing HP is the way to increase the amount of HP Stoneskin has. DEF/MDEF in general don't make a whole lot of difference when it comes to the damage you receive from attacks to be honest. It's a flat reduction in damage meaning:
Mob hits 2000 with 0 DEF, mob hits 1500 with 500 DEF. However there are Crit multipliers and other multipliers that may be taken before DEF is taken so it's not always the same amount of reduction. Also the amounts are just examples but I think it's probably kind of around that anyways. So it's effective for most regular mobs as they usually hit small numbers, but not for bosses as they hit big numbers.
Melee+Magic Res are the main way to reduce the damage you take from bosses as they are a % damage decrease. So if you have 10% melee resistance and a mob does a melee attack that hits for 2000 without resistance then you will take 1800 instead. Not very effective for regular mobs as they hit small numbers(although their damage is completely insignificant to Enchanters) but will be very effective for a boss that hits for 20k damage as it will reduce the amount to 18k. This is also why your Stoneskin lasts longer with a Bishop because they have Aegis 3(50% Magic Res, may just be 50% magic damage reduction, as in it's applied after normal magic resistance). You will experience the same thing with a Monk or Servant in the party although to a lesser extent slightly(40% instead of 50%). You also won't notice a difference on certain bosses that do more melee attacks(WoL comes to mind) however for the most part those do a little less damage anyways.
Unless somethings been released in the past month, Wound Transfer, Katzbalger, Dragon Roar, and Ama No Habakiri are all good for Raton. Katzbalger UP will probably be best(Neutral Res applies to both melee and magic since he is Neutral ele).
Basic cheap set to allow you to tank Raton better would be Katz II, Barbarotita, Licht Armor, Wisdom Bangle. However you are trying to solo so you may need more damage than that. Best I can think of for damage+survivability would be:
Dragon Roar, Ideasol(or something with HP and MATK), Hulam Nemes or Excelis Re UP, and Wisdom Bangle or Dnewt Mezza if you can manage the HP. You also want pots that give you the "Max HP" buff to cancel his debuff to keep your max HP high.
Tadah long post haha. Now you know the mechanics behind Stoneskin from what I know so far.
