From what you're saying, I don't have any doubt that you'd enjoy a quick change tool post of any description. If height adjustment is your biggest headache, I'd say the same thing I did when you were asking a similar question this summer. I think you should look into a DIY Norman style tool post. They are kind of their own thing, not a quick change, not a lantern/rocker, not a four way without significant effort (although you could more than likely make a very nice three way post out of it, reserving the fourth side for the locking bolt). I think that would do what you are looking for. There's any number of examples of them posted here, and all over the internet. You need not use an existing design, you can make it as you wish. Crude but effective (as mine is), all the way up to very fancy and refined. The first holder you make will take forever while you figure it out, after that they're really not too difficult. You'd (probably) have to buy in the bolt and set screws, but the entire thing, start to finish, can be made with very simple tools. You'd need an end mill, two taps and tap wrench, a hack saw, a drill, and a few drill bits, and your lathe. The lathe will do the bulk of the work. It's daunting when you first look at it, but each step is pretty simple.
If you do decide to buy in a quick change tool post, The Aloris style will be the easiest (or equal) to get mounted and set up, and offer you all of the adjustability that you are looking for. The Multifix will be somewhat more involved to set up (probably, not necessarily), it won't offer you any more positions or positionability. What the multifix offers is more "preset" positions available without rotating the tool post. In practice, the difference between moving the tool holder to a new position, or rotating the tool post is only where you put your hand when you loosen it. If I was going to go that route (I'm not at this time, but if I was going to), I'd probably pony up for the wedge style, not the plunger style on the post it's self, at which point the tool holders can be bought in as needed, they're fairly easy to make IF you have a mill, or dirt cheap to buy, they come in all kinds of configurations for different tools. I just don't have enough predictable work to make any tangible time or effort gains from the fixed angular adjustments of the Multifix types. That takes production line work before you'll ever get ahead for having that feature.
You said you found packs of shims just for this purpose- You said you don't mind swapping tools in the four way tool post you currently have- Would it solve the issue for you if you just super glued the correct amount of shims under your current tool bits, so that each tool bit was already correctly shimmed, every time?
