It's an interesting idea, but banning superior tech like that doesn't work for me It would actually make sense to me that the globes made the engines more efficient - maybe they were a part of the process that allowed the switch from lithium to dilithium.
Not wanting to do your ideas down (), can I suggest an alternative explanation for the apparent change in speeds? I first came across this one on the Star Trek Cartography website, which has some interesting speculation about distances and speeds.
The basic theory is based on the mention (in the TNG Tech Manual) of warp speeds being affected by the "Cochrane factor" which is the relative density of subspace in the location. The idea is that there are regions of space where the density is such that a ship can travel much faster than might be obvious (1000-10000 times faster!). These areas often form channels between certain locations (such as Earth to Q'on'oS), which makes travel much simpler IF you know where the channel is... This explains NX-01's four day trip to the Klingon homeworld nicely, and the DS9 Earth-Bajor trip, and also much of the TOS inconsistencies.
TNG and later often had ships travelling routes other than those channels affected by this, hence the vessels seem to be much slower.
As an aside, it also explains why the Vulcan star charts are so important in Enterprise, when we already (in the 21st century) know where every star within a couple of hundred light years is! Starfleet at the time simply did not have the technology to detect the channels. By Kirk's time they did.
Your other points are actually outside the realm of the Spacedock manuals, but...
It's not unreasonable to assume that the TNG Federation restricts the use of most lie detection technology (psychotricorders and so on) as an invasion of privacy. Remember it's a very "touchy-feely" organisation, and will be big on rights.
Time travel definitely exists, but it's use is all but forbidden. After Kirk's depradations, the Temporal Prime Directive is in full force, and Lucsly and Dulmer's organisation will ensure nobody pfaffs around with something as inaccurate as the temporal slingshot!
The computer's transporter antics are difficult to explain, but the original Enterprise did have both Scotty and Spock aboard, both of whom were slightly better than later examples of their craft
Welcome to the boards btw, I hope you understand we just love debating things - we do appreciate your input
Jon
"There are worlds out there where the sky is burning, where the sea is asleep and the rivers dream; people made of smoke and cities made of song.
Somewhere there's danger, somewhere there's injustice, and somewhere else the tea is getting cold. Come on, Ace, we've got work to do."
THE DOCTOR, "Survival" (Doctor Who)