I like the idea behind the puzzle (I like it a lot more than the runework of 4.0) but I have a few problems with it:
1) Since Research Points are so difficult to come by now, it's easy to run out of Research Points now. Before, you could theoretically use a maximum of 2 Research Points of each type of Aspect in a given research, if you wanted, by simply using one to unlock the Aspect so you know which runes it uses, and then moving them around as you see fit (after Research Mastery, of course) which just uses up Ink, and then using the second point to reactivate it once all the runes are in place. So you rarely ran out of Research Points - not only did you earn a lot more and didn't have a soft cap as you filled up your Research Points, but you could use a lot fewer Research Points while researching. Now, you end up needing more than 2 Research Points per Aspect in a given research (although you can typically avoid using the ones actually used in the research, since you just have to connect to them, and for that you can use their components), and also have less Research Points to begin with. The Deconstructor is basically useless for getting Aspects (higher-tier Aspects can use upwards of 12 or 16 total Primal Aspects to combine up to them) since you have to sit there and clear the table every time it finds a single Primal Aspect.
2) While Research Expertise and Research Mastery make it easier to remember the Aspects' relationships, they aren't foolproof. First, Research Mastery's ability does not work if you've emptied the Research Point you want to make. So if you end up with 0 Humanus, then you can't Control+Click it to make a Humanus from extra Cognitio and Bestia, even if you have the Aspects. You have to actually hover over Humanus, see that it uses Cognitio and Bestia, and manually combine them. Likewise, if you're out of Bestia, you can't make Humanus even if you have the Motus and Victus needed to make Bestia, so even if you do have at least 1 Humanus and want to make more and could do so, you might still have to hunt for the two Aspects that make up Humanus to see which one you're actually out of so you can make more of that (and you can't Control+Click it either, due to the previously mentioned issue). Finally, even though Research Expertise lets you know what two Aspects make up a given Aspect, they don't tell you what a given Aspect can combine to make - and with the Research the way it is now, you want to know both what it is made from and what it can be made into, since both will connect on the Research. An Aspect can only be made of two things (for instance, Humanus being made from Cognitio and Bestia), but they can often be made into multiple things - Humanus into Lucrum, Instrumentum, Meto, Messis, and Perfodio!
I had an idea for a more interesting Research method, which I posted on reddit in my Thaumcraft Aspect chart thread. Let me describe my idea here. Maybe Azanor will see it and think it interesting enough to start with.
First, instead of having a Research Table, you will craft a Research Lab. Perhaps this can be a multiblock - make it from 1x Crucible and 1x Crafting Table and then right clicking on the Crafting Table with a Wand. Someone suggested being able to add things to the Research Lab as you go, so that could be an interesting idea, as well.
The left side of the Research Lab is a specialized Essentia Boiler - something like an Arcane Furnace + Arcane Alembic combined. When you open it, you will have a section for Fuel (to power to melting process, just like an Arcane Furnace, although it would likely be best if it was less efficient) and a section for items (which are melted down into Essentia automatically). The Essentia stays inside the Research Lab, and it can store a maximum of 16 units of Essentia of varying types (so it will have a liquid-storage indicator that can fill with different Essentia - you could have 8 of one and 8 of another, or 16 of one, or 2 of a bunch of Essentia, whatever - it would show the essentia in layers). Clicking on an Essentia will bring that Essentia to the "top" of the Essentia Boiler, which is the one that will be used. You can right-click on the Essentia Boiler with a Warded Jar to put the topmost Essentia into that Warded Jar (if the Jar is empty or the same type) just like an Arcane Alembic, and Essentia in the Boiler can also be piped out (or in) if necessary. You can also right-click on Essentia while in the Boiler's GUI, which will release that Essentia into the air as Flux Gas - this is useful early on, if you need different Essentia to do your Research, but don't have Warded Jars yet.
That brings me to the right side of the Research Lab. This is the Thaumic Laboratory. Here, you can put Research Notes that you've obtained from selecting them in the Thaumonomicon or from a discovery. The mini-game is the same as in Thaumcraft 4. However, now, instead of using Research Points (which are no longer a thing) you use Essentia from the Essentia Boiler. Clicking on the Research hexes will use the topmost Essentia from the Essentia Boiler to infuse that part with the corresponding Aspect Rune. (If possible, we can have the Boiler and Laboratory all in the same GUI, since you can replace the majority of the "Research Points" section of the current Research Table with the Boiler portion). In addition, a shortcut to the Thaumonomicon should be available at the Thaumic Laboratory, even if the player does not have their Thaumonomicon with them at the time - this way, they can select their Research and make Research Notes (provided they have Scribing Tools and Paper of course) and check the List of Aspects right from the Laboratory.
That's my idea, anyway. Research Points would be gone - a Thaumometer would be useful only for telling you what Aspects you can get from any given item (and also give you a chance at revealing hidden research, or giving you Research Notes) and for determining Aura Node values, as well as telling you how much of each Aspect you have in Essentia Jars and so on.