Although speakers are not exactly my forte, no-one else has answered this yet and it is about to disappear off the list of 100 most recent posts, possibly never to be seen again, so I will pass a few comments in the hope that it might help.
It is uncertain what you mean by "sanity check", but maybe these comments might help with your confidence, as you say that this is your first attempt at a X'over. You don't say how you have arrived at this design, whether it has been copied from elsewhere, or whether you have made some calculations to arrive at the result, so I hope I am not just "teaching my grandmother to suck eggs" here.
The overall circuit diagram is fine for a conventional second-order, two-way X'over design. It is normal to have a series choke and a shunt capacitor for the woofer as you have shown, and a series capacitor and shunt inductor for a tweeter. Therefore, it is not likely that you will end up damaging anything, or whatever, if you try this schematic out.
The additional 8R resistor in series with the 10uF cap (with this combination being in parallel with the woofer) is also not unusual, and will contour the response of the woofer somewhat, if this is what you desire here. Also, the addition of the 4R resistor in series with the tweeter will affect the X'over point somewhat and will reduce the output level of the tweeter, which would be desirable if the tweeter is more sensitive (more efficient) than the woofer.
However, good crossover design is a highly-skilled exercise, and carefully-calculated components often (usually, in my experience!) end up being changed during subsequent developments by a factor of up to twice, or maybe one half, of any theoretically correct value components, so do expect to do quite a lot of experimentation before being fully satisfied with any results.
I won't comment on any component values which you have shown since they will depend entirely on so many factors like the characteristics and efficiency of the drivers, themselves, and how these drivers are mounted and 'loaded' in their intended enclosure, and this is beyond the scope of a quick reply like this.
Depending on your interest, I would urge you to read all that you can about this fascinating subject (I built my first speaker/X'over nearly 50 yrs ago, and I am still learning!) but in the end, a lot of patient empirical development work will be necessary to achieve the best results, and I guess that (most?) other speaker designers would agree with this.
Bsically I am just seconding what the earlier post has said.
Your crossover will work in that it will preven low frequency energy destroying the tweeter and will reduce high frequency output from the woofer.
This will give you a speaker that doesn't sound completely broken. However as mentioned in the eralier post it is unlikely to give you something that sound really good as that takes measurement equipment and lots of patience. Or no measurement equipment, very good ears and lots and lots and lots of patience.
So if you just want to have a go, this will work. One of the great things about designing speakers is you very rarely end up with something that doesn't work. But getting the sound you want that can take forever.