Ok, you have kinda the right idea, but going the wrong way about it. It can be a little confusing though. so i can understand why.
First of all, when Fury says that you need to know your drivers' frequency response, he doesn't mean the 'frequency response' specification listed on the spec sheet or in the manual. This simple set of numbers are usually completely un-standardised, and as such they tell you pretty much nothing at all about a speaker. The upper and lower limits are pretty much always WAY overrated - especially with car speakers.
What you actually want, is a frequency response
chart. It's basically a measured graph, which shows frequency (hz) across the horizontal axis, and output (dB) accross the vertical axis.
This gives you a far more usable data, because you can determine exactly when the driver starts to roll off (or beome erratic) and select an appropriate crossover point to cut the driver off before that occurs.
For example, here is a frequency response chart for the HAT L3 you are running:

HAT claims 140hz - 10khz usability for this driver, but as you can see it's about 5dB - 6dB down at 140hz, making it very much
not recommended to be used this low. As far as frequency goes, it's only flat down to about 200hz, so based on FR alone this is the lowest you would cross (though high distortion would lead to me shifting to at least 400hz, personally).
On the top end it can genuinely play toi to 10khz, but only barely - the instant it passes 10khz it drops off almost like a shelf. Even the slightest degree off axis, and the top end of that chart would change dramatically - probably starting to drop off around 6k-7k. Not that you'd even know, because HAT have nicely not provided an off axis response...meaning that unless the driver is absolutely 100% on axis, finding the upper FR limitation is pretty much guess work.
At least they have actually provided a chart of some kind though - majority of car audio companies do not, which picking the right frequency pure guess work.
Anyhoo, the next problem is frequency response is really only a small part of the equation when determining crossover points. Just as important (if not moreso) is distortion. All drivers produce what's called non-linear distortion. How it works and where it comes from is a bit of a complicated point so I'll save that for now, but the important thing to know is that it sounds nasty. Basically, it's what makes a driver harsh of uncomfortable to listen to over long periods of time, or (if it's really bad) immediately. All drivers have distortion, but playing a driver outside of it's comfort zone (i.e. too low or too high) can increase distortion dramatically. A tweeter could be absolutely clear as day crossed at 4khz, but then crossing that same tweeter at 2khz could cause distortion at all frequencies to increase to dramatic levels.
So, this is the next thing you need to consider with a crossover - the frequency response chart on it's own isn't enough to go by. Perfect example, the infamous Vifa XT25 is has a near ruler flat frequency response that extends right down to about 1khz...going purely off the FR chart, you'd swear that you could cross this tweeter at 1.6khz no problems at all...but don't ever do it. The XT25 has exceptionally low distortion from 3khz up, moderate distortion at 2.5khz, and terrible distortion at 2khz and under. Not only would crossing at 1.6khz create a very uncomfortable sound over long periods of time, it would also dramatically increase the risk of damaging the tweeter - don't do it!
This is why I am always skeptical about car audio drivers - they rarely provide so much as a Frequency Response chart, and even those who go that far
never provide distortion charts. I think Dynaudio's Esotar drivers are the only ones i've seen distortion graphs provided for. This makes me sceptical because taking distortion measurements is not THAT hard for a million dollar speaker manufacturer who already has the measuring equipment...so by not providing the data, what are they trying to hide? If the drivers were truly stunning in those results, surely they'd be flaunting the results at every opportunity, right?
But anyways, to sum it up the details you're looking for when setting crossovers are a combination of frequency response, and distortion. There could be other smaller factors, but these are the big ones.
Also to answer your other question, would you overlap crossovers? Generally no. The only time I would ever overlap drivers (either via crossover point or slope) is if it's absolutely necessary in order to make up for a deficiency of a particular driver. For example, if your midbass simply doesn't play low enough, so you're overlapping your sub a little to make up for it. People do this often, and it rarely gives good results - usually it's a case of trading one evil (response gap) for another (response peak) and very rarely do they work out well. On the odd rare occasion, a drivers natural rolloff may combine with the increasing slope of the other driver to magically produce a nice smooth transition but this is quite rare unless it's specifically planned. General rule for me is don't overlap, and if your drivers can't cover those frequencies get some that can.
Sorry for the length of the post, but hopefully some of it will offer you some insight