Wow there is a lot going on here
yes we would print / flash/ print the hoodie you detail.
There are a couple of things you need to think about / try / guess at /
1 make sure you have sufficient tack to hold the hoodie in place, we even renew the tack with each hoodie load especially if the logo is a full size print. You will find the lower areas of a large print will not line up if you do not really get the hoodie stuck down. Not so important on a left chest.
2 do not overflash your hoodie, it will shrink (polyester threads) so don't get it too hot
3 take your 110 mesh up to at least 35 newtons, 22 is way too soft and keep your off contact to no more than 1/8 inch with a 35newton stretch.
4 half tones are going to be a problem with a double hit and a 110 screen test print to see what you get.
It is some extra work but we might even double screen the white one for the half tone and one for the finish white. Those with more experience will have a better suggestion but in a fire fight to make it work we would burn 2 screens just in case the all in one did not work.
5 some like to run the hoodie under the flash before you print your first color to get the hoodie to shrink what ever it is going to shrink from the heat before you print.
6 make sure the hoodie is cool before you print the next color or white hit
7 re-read step 3
8 get some other opinions I am round the bend more time than not
mooseman