Hmmm a lot to cover here. Let’s see …
One thing you can try is instead of Vase mode, print with 2 walls and zero top layers. Depending on what you’re printing of course. That gives you the same effect but a thicker surface.
Next. Trying to get a .8 wall out of a .4 nozzle is … problematic. In theory you can, ITRW not so much, as you’ve found.
A .6 or .8 nozzle is the ultimate answer. A lot of people are switching to .6 as the standard now that printers are able to push the plastic faster. I run .6 unless I need a really detailed print. Any Vase mode stuff - .6 or .8.
Are you running OrcaSlicer? Sounds like you’re using Studio. Studio is great software, but for many things OrcaSlicer is better when you’re trying to push the edge. I’m fairly active on here so I often forget whom I’ve suggested this to but you might take 5 mins and read this (Click the Blue Link):
Don’t feel like it’s “another thing to learn” - OrcaSlicer is 95% the same, but it has Calibrations that let you fine tune that BL Studio doesn’t. Looks and acts the same. When you’re right at the edge of what’s possible, that can be the difference you need and it’s free to try.
On “getting a .6 or .8 nozzle” - Yeah, do so, particularly the .6. But also buy a Fan, Heater, and Thermistor as well. That will let you assemble a “plug and play” full hotend that makes swapping a breeze. They’re very reasonably priced and will kick you up high enough to get free shipping.
You also get three heaters and three thermistors for the price, which can be handy if something goes south. 
They do fail, usually at a most inopportune time, life taking a shot at ya!
Cooling - Yeah, that can be killed easily enough and a quick print of say 10 layers will give you an idea of how it’s going.
For a .4 nozzle … trying to be polite here but, yeah. Seriously - get OrcaSlicer and if you have it run at least these four calibrations and save it as a new Filament Profile
- Flow Rate, 1st one.
- Pressure Advance
- Max Flowrate (different)
- Temp Tower.
Do them in that order. I usually skip the Flow Rate 2 test (not Max) have yet to see it help.
I strongly suggest you invest the time to do these test on any new reel you get if it’s a new Brand. Sometimes a new color of a new brand will need it too. Plastic formulas vary.
The joy of dropping in a reel, choosing your customized profile, and knowing what you print is going to work is fabulous. 
It will also let you maximize speed. I had a print on a filament I couldn’t get to work for the life of me. I ran those tests and when I printed it was so good I found I could run on Ludicrous mode!
The print went from 1:48 to being done in 1:04 (hours). That’s quite a savings. The part looked great too. My Wife was astounded. (She’s pretty 3D savvy). Me too.
That’s all for now, hope it helps some.
Cheers!