Cool! Here is the INTENDED behavior for what happens to your stats, skills, levels, items, and gear upon death and Reincarnation.
HOW STAT/SKILL/EQUIPMENT PRESERVATION IS SUPPOSED TO WORK (For The Immortal Shadow)
When you die , you lose 1 level and most of your skills. When you Reincarnate, you gain +50 jp to spend for each level beyond your first. Your AP allotments should persist. HALF of any RESOLVE loss/INTELLECT gain from learning spells should persist (a last minute balance change was made to change this from all to half, because I got tired of Reincarnating in a new Vessel with a starting Resolve score of like 3 because I had stupidly learned like every spell possible as the last Vessel, and thought players would too). Skills learned from the Egyptian Pantheon should not be lost when you die and Reincarnate (if you bought Blessing of Bast through the Learn Skills menu, it will be lost, but if you received it from Bast herself in Egypt, you'll still have it).
When you die, you lose all of your equipment and items. When you reincarnate into a different Vessel, you receive bonus starting cash based on your Reincarnation Count. For Checkpoint A1, for instance, this is Reincarnation Count x $250. If you reincarnate into the SAME Vessel, you receive that bonus cash, plus ADDITIONAL bonus cash based on your level. For Checkpoint A1, for instance, you receive ADD'L bonus cash equal to your Level x $250. So reincarnating into the same Vessel (say a Level 10 Academic) at Checkpoint A1 with say 2 Reincarnations under your belt, you should have bonus cash of $3000 ($250 x 2 Reincarnations + $250 x 10 Levels). This money can be spent at the Bazaar to get you closer to the power level you were at before you died, but also lets you experiment with new items and equipment.
HOW LOOT POINTS AND REINCARNATION ARE SUPPOSED TO INTERACT
Any loot you collect from an area in the same Investigation will NOT respawn when returning to that Investigation (irrespective of Vessel). This is by design. Instead, depending on your Reincarnation Count and some other hidden factors, new, weirder, and better loot may spawn in the previous areas. This is meant to enhance replay value, a concept I think comes into play in EREWHON well before you actually clear the game.
So zutsu13, what this boils down to is that the answer to your issues with feeling naked and underpowered upon Reincarnating as the Academic on 2F can be rendered in a single word: Bazaar!. You should have noticed that you Reincarnated with a fair bit of cash to a TON of cash depending on your level. You also should have some of the items Malphus will take to open a portal to the Bazaar in your inventory, if you are the Academic (didn't give the Occultist this grace, I think, because he can MAKE those items). Even if not, I believe that when you Reincarnate to this checkpoint, Gabrielle's equipped weapon will also pay for opening the portal. So, go through the portal to the Bazaar, and gear up. (Don't accept the Mad Arab's gift lightly, should it be offered.)
Unless of course there's another bug that I didn't see on my last pre-alpha playtesting runs: always a very real possibility!
Let me know if the Twins keep being a nightmare and I can tell you the correct sequence of dialogue approaches in the "Social Combat" scene as the Academic to get them to not try to murder you. (As the Occultist, you can simply bypass fighting them if you have seen the Yellow Sign and tell them that you are "chill/down with Hastur, so to speak'....this approach might have SAN consequences.) Another tip hopefully not too obvious to be worth mentioning: you can and should absolutely heal and buff as best you can during the "Social Combat" sequence. As long as you take no direct aggressive action, this won't cause them to attack you. Well, more than they're already attacking you, I mean. The first phase of the combat (before they separate) is sort of both sides playing "kitten mittens": the Twins will buff, heal, and try to toss some status effects on you, but won't generally hit you for damage. If you reflect that strat during Social Combat, you'll be able to keep talking.
So one of the reasons I left the Twins encounter so tough, even though it's the first real boss fight of Investigation A, is that it's also, strictly speaking, an OPTIONAL boss fight, whether playing as the Academic or the Occultist, it is possible to talk them down.