Pardon the thread necromancy, but I'm late to the game and I have to get this off my chest...
Jim - You aren't seriously considering these rules changes, are you? These seem more like after-the-fact "house rules" applied to what is, in my opinion at least, an already extremely well written and thought-out set of rules.
* Constitution determines what die you use for rolling hit points...
I'm not sure how this is any "better" than the current rules. I understand your desire to see more "low" throws for hit dice, but they are there in the current rules... unless one is cheating.
* Magic saving throws modified by Charisma...
Makes some sense I suppose, if your concept of how magic works in your game is that it is purely a function of the caster's will. But, given that the spell rules are decidedly old-school Vancian, it seems more appropriate to use Intelligence. (Personally I prefer no bonuses at all - use the tables as is. Although, I do like LotFP's take on Wisdom being sort of "luck" bonus for non-magical saves - perhaps have it apply to all saves?)
* Shields should give bonuses to parrying...
Might be good to add some more options to combat, but I think this needs to be ironed out a bit first. Shields already give a bonus to AC... which is, in essence, a "parry bonus".
* Encumbrance should affect initiative in some way...
I love the Encumbrance rules in LotFP; they're fast and easy. So why not make this one fast and easy too? Characters that are heavily encumbered or worse go last in the round... period.
* Not original, but all weapon damage is d8, with the "roll twice, take the lowest/highest" for certain kinds of weapons.
Sort of like the original "all weapons do 1d6", but house-ruled to satisfy those players who complain that a halberd would do more damage than a prison shiv "in real life". I like using lots of different dice for weapon damage myself. One die, one number, done. And it makes the halberd-vs-shiv crowd happy.
* Also thinking that by expanding the skill list a bit...
That word. Skillz. Blarg! I love the idea of the Specialist (reminds me of the "Other" career in classic Traveller), but I also like that those "skills" are isolated to the Specialist, and all other classes are 1 in 6 for anything.
On an opinionated side note: I could go on and on about how I feel that the hobby was destroyed in part by the idea of skills and customized characters, but I won't. I'll just say that the most memorable characters for me were not numbers on a character sheet; it was how they were played and how they developed in the campaign that made them memorable.
* Witch-Hunter, etc...
I think these sorts of things are best left for a supplement. I think it makes it easier for the referee to preclude them if they aren't staring the players in the face on the pages of the core rule book. And for what it's worth, any imagined archetype can be played using just the four core "human" classes. A Witch-Hunter is just a Cleric or Fighter. If I wanted to be a Witch-Hunter, I would roll up a Cleric and say "I hate witches and demons, and I'm going to use a cross-bow... with silver bolts." Same goes for the "explorer", after all, isn't that what all the character do already?
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TL/DR section:
If it ain't broke, don't fix it.